diff --git a/src/finiteVolume/fvMesh/fvMeshSubset/fvMeshSubsetProxy.C b/src/finiteVolume/fvMesh/fvMeshSubset/fvMeshSubsetProxy.C
index 302357e8ba..1e6f080cd9 100644
--- a/src/finiteVolume/fvMesh/fvMeshSubset/fvMeshSubsetProxy.C
+++ b/src/finiteVolume/fvMesh/fvMeshSubset/fvMeshSubsetProxy.C
@@ -160,7 +160,7 @@ bool Foam::fvMeshSubsetProxy::correct(bool verbose)
             Info<< "Subsetting mesh based on cellSet " << name_ << endl;
         }
 
-        cellSet cset(baseMesh_, name_);
+        cellSet cset(baseMesh_, name_, IOobject::NO_REGISTER);
 
         selectedCells.resize(nCells);
         for (const label idx : cset)
diff --git a/src/meshTools/topoSet/cellSources/cellToCell/cellToCell.C b/src/meshTools/topoSet/cellSources/cellToCell/cellToCell.C
index 667ccd02c3..c175d121d2 100644
--- a/src/meshTools/topoSet/cellSources/cellToCell/cellToCell.C
+++ b/src/meshTools/topoSet/cellSources/cellToCell/cellToCell.C
@@ -114,7 +114,7 @@ void Foam::cellToCell::applyToSet
             }
             else
             {
-                cellSet loadedSet(mesh_, setName);
+                cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
                 set.addSet(loadedSet);
             }
         }
@@ -136,7 +136,7 @@ void Foam::cellToCell::applyToSet
             }
             else
             {
-                cellSet loadedSet(mesh_, setName);
+                cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
                 set.subtractSet(loadedSet);
             }
         }
diff --git a/src/meshTools/topoSet/cellSources/faceToCell/faceToCell.C b/src/meshTools/topoSet/cellSources/faceToCell/faceToCell.C
index a71a70760b..848851ffa5 100644
--- a/src/meshTools/topoSet/cellSources/faceToCell/faceToCell.C
+++ b/src/meshTools/topoSet/cellSources/faceToCell/faceToCell.C
@@ -146,8 +146,7 @@ void Foam::faceToCell::combine
     else
     {
         // Load the set
-        faceSet loadedSet(mesh_, setName);
-
+        faceSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& faceLabels = loadedSet;
 
         combineImpl(set, add, faceLabels);
diff --git a/src/meshTools/topoSet/cellSources/haloToCell/haloToCell.C b/src/meshTools/topoSet/cellSources/haloToCell/haloToCell.C
index 9c08a2e3f2..ba70c4bcb9 100644
--- a/src/meshTools/topoSet/cellSources/haloToCell/haloToCell.C
+++ b/src/meshTools/topoSet/cellSources/haloToCell/haloToCell.C
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2019-2022 OpenCFD Ltd.
+    Copyright (C) 2019-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -83,9 +83,11 @@ void Foam::haloToCell::combine(topoSet& set, const bool add) const
     // The starting set of cells
     bitSet current(cells.size());
 
-    if (isA<topoBitSet>(set))
+    const auto* topoBitsPtr = isA<topoBitSet>(set);
+
+    if (topoBitsPtr)
     {
-        current |= refCast<const topoBitSet>(set).addressing();
+        current |= topoBitsPtr->addressing();
     }
     else
     {
diff --git a/src/meshTools/topoSet/cellSources/pointToCell/pointToCell.C b/src/meshTools/topoSet/cellSources/pointToCell/pointToCell.C
index 9c74f9e3e6..aad09d4423 100644
--- a/src/meshTools/topoSet/cellSources/pointToCell/pointToCell.C
+++ b/src/meshTools/topoSet/cellSources/pointToCell/pointToCell.C
@@ -126,8 +126,7 @@ void Foam::pointToCell::combine
     else
     {
         // Load the set
-        pointSet loadedSet(mesh_, setName);
-
+        pointSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& pointLabels = loadedSet;
 
         combineImpl(set, add, pointLabels);
diff --git a/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.C b/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.C
index f192b4f37d..26270cf1ef 100644
--- a/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.C
+++ b/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.C
@@ -351,8 +351,7 @@ void Foam::regionToCell::combine(topoSet& set, const bool add) const
         if (isZone_)
         {
             Info<< "    Using cellZone " << setName_
-                << " to delimit search region."
-                << endl;
+                << " to delimit search region." << nl;
 
             selectedCell = false;
             for (const label celli : mesh_.cellZones()[setName_])
@@ -363,10 +362,9 @@ void Foam::regionToCell::combine(topoSet& set, const bool add) const
         else
         {
             Info<< "    Loading cellSet " << setName_
-                << " to delimit search region."
-                << endl;
+                << " to delimit search region." << nl;
 
-            cellSet subSet(mesh_, setName_);
+            cellSet subSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             selectedCell = false;
             for (const label celli : subSet)
@@ -428,14 +426,14 @@ Foam::regionToCell::regionToCell
     ),
     nErode_(dict.getCheckOrDefault<label>("nErode", 0, labelMinMax::ge(0)))
 {
-    // A single set or zone only!
-    if (dict.readIfPresent("set", setName_))
+    // A single "set" or "zone" only
+    if (!dict.readIfPresent("set", setName_))
     {
-        isZone_ = false;
-    }
-    else if (dict.readIfPresent("zone", setName_))
-    {
-        isZone_ = true;
+        // Optional entry
+        if (dict.readIfPresent("zone", setName_))
+        {
+            isZone_ = true;
+        }
     }
 }
 
diff --git a/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.H b/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.H
index 2dd718a81b..ae22b4a3ab 100644
--- a/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.H
+++ b/src/meshTools/topoSet/cellSources/regionToCell/regionToCell.H
@@ -73,7 +73,7 @@ Usage
       source     | Source name: regionToCell           | word |  yes  | -
       insidePoints  | Coordinate(s) that is inside connected region <!--
                                              --> | vectorList |  yes  | -
-      set        | Name of cellSet giving mesh subset  | word |  no   | none
+      set / zone | Name of cellSet / zone giving mesh subset  | word |  no | -
       nErode     | Number of cell layers to erode mesh to detect holes <!--
            --> in the mesh - set to 0 if not used      | label | no   | 0
     \endtable
diff --git a/src/meshTools/topoSet/cellSources/targetVolumeToCell/targetVolumeToCell.C b/src/meshTools/topoSet/cellSources/targetVolumeToCell/targetVolumeToCell.C
index 81f0710165..2d7aa87f01 100644
--- a/src/meshTools/topoSet/cellSources/targetVolumeToCell/targetVolumeToCell.C
+++ b/src/meshTools/topoSet/cellSources/targetVolumeToCell/targetVolumeToCell.C
@@ -133,13 +133,13 @@ void Foam::targetVolumeToCell::combine(topoSet& set, const bool add) const
                 << maskSetName_ << endl;
         }
 
-        maskSet = false;
-        cellSet subset(mesh_, maskSetName_);
-
+        cellSet subset(mesh_, maskSetName_, IOobject::NO_REGISTER);
         const labelHashSet& cellLabels = subset;
+
+        maskSet = false;
         maskSet.setMany(cellLabels.begin(), cellLabels.end());
 
-        nTotCells = returnReduce(subset.size(), sumOp<label>());
+        nTotCells = returnReduce(cellLabels.size(), sumOp<label>());
     }
 
 
diff --git a/src/meshTools/topoSet/cellZoneSources/setToCellZone/setToCellZone.C b/src/meshTools/topoSet/cellZoneSources/setToCellZone/setToCellZone.C
index ca3d0c1d78..d12ccf64fe 100644
--- a/src/meshTools/topoSet/cellZoneSources/setToCellZone/setToCellZone.C
+++ b/src/meshTools/topoSet/cellZoneSources/setToCellZone/setToCellZone.C
@@ -114,12 +114,12 @@ void Foam::setToCellZone::applyToSet
             }
 
             // Load the sets
-            cellSet fSet(mesh_, setName_);
+            cellSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             // Start off from copy
             DynamicList<label> newAddressing(zoneSet.addressing());
 
-            for (const label celli : fSet)
+            for (const label celli : loadedSet)
             {
                 if (!zoneSet.found(celli))
                 {
@@ -139,7 +139,7 @@ void Foam::setToCellZone::applyToSet
             }
 
             // Load the set
-            cellSet loadedSet(mesh_, setName_);
+            cellSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             // Start off empty
             DynamicList<label> newAddressing(zoneSet.addressing().size());
diff --git a/src/meshTools/topoSet/faceSources/cellToFace/cellToFace.C b/src/meshTools/topoSet/faceSources/cellToFace/cellToFace.C
index d3b7508de7..1777c0de56 100644
--- a/src/meshTools/topoSet/faceSources/cellToFace/cellToFace.C
+++ b/src/meshTools/topoSet/faceSources/cellToFace/cellToFace.C
@@ -221,11 +221,11 @@ void Foam::cellToFace::combine
         // Load the set
         if (!exists(mesh_.time().path()/topoSet::localPath(mesh_, setName)))
         {
-            SeriousError<< "Cannot load set "
-                << setName << endl;
+            SeriousError
+                << "Cannot load set " << setName << endl;
         }
 
-        cellSet loadedSet(mesh_, setName);
+        cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& cellLabels = loadedSet;
 
         combineImpl(set, add, cellLabels);
diff --git a/src/meshTools/topoSet/faceSources/faceToFace/faceToFace.C b/src/meshTools/topoSet/faceSources/faceToFace/faceToFace.C
index 9eaed67c4e..ef1cc9cdac 100644
--- a/src/meshTools/topoSet/faceSources/faceToFace/faceToFace.C
+++ b/src/meshTools/topoSet/faceSources/faceToFace/faceToFace.C
@@ -114,7 +114,7 @@ void Foam::faceToFace::applyToSet
             }
             else
             {
-                faceSet loadedSet(mesh_, setName);
+                faceSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
 
                 set.addSet(loadedSet);
             }
@@ -137,7 +137,7 @@ void Foam::faceToFace::applyToSet
             }
             else
             {
-                faceSet loadedSet(mesh_, setName);
+                faceSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
 
                 set.subtractSet(loadedSet);
             }
diff --git a/src/meshTools/topoSet/faceSources/holeToFace/holeToFace.C b/src/meshTools/topoSet/faceSources/holeToFace/holeToFace.C
index 90781958d5..9b70b6698e 100644
--- a/src/meshTools/topoSet/faceSources/holeToFace/holeToFace.C
+++ b/src/meshTools/topoSet/faceSources/holeToFace/holeToFace.C
@@ -1148,7 +1148,7 @@ void Foam::holeToFace::applyToSet
     bitSet isBlockedFace(mesh_.nFaces());
     for (const word& setName : blockedFaceNames_)
     {
-        const faceSet loadedSet(mesh_, setName);
+        faceSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         isBlockedFace.setMany(loadedSet.begin(), loadedSet.end());
     }
 
@@ -1158,7 +1158,7 @@ void Foam::holeToFace::applyToSet
     {
         for (const word& setName : blockedCellNames_)
         {
-            const cellSet loadedSet(mesh_, setName);
+            cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
             isCandidateCell.setMany(loadedSet.begin(), loadedSet.end());
         }
     }
diff --git a/src/meshTools/topoSet/faceSources/pointToFace/pointToFace.C b/src/meshTools/topoSet/faceSources/pointToFace/pointToFace.C
index 6a4a77b96e..4c2f35d51e 100644
--- a/src/meshTools/topoSet/faceSources/pointToFace/pointToFace.C
+++ b/src/meshTools/topoSet/faceSources/pointToFace/pointToFace.C
@@ -172,8 +172,7 @@ void Foam::pointToFace::combine
     else
     {
         // Load the set
-        pointSet loadedSet(mesh_, setName);
-
+        pointSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& pointLabels = loadedSet;
 
         combineImpl(set, add, pointLabels);
diff --git a/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.C b/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.C
index 683e5e68e0..e35793c8dd 100644
--- a/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.C
+++ b/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.C
@@ -146,7 +146,7 @@ void Foam::regionToFace::combine
     if (verbose_)
     {
         Info<< "    Loading subset " << setName_
-            << " to delimit search region." << endl;
+            << " to delimit search region." << nl;
     }
 
     indirectPrimitivePatch patch
@@ -236,12 +236,10 @@ Foam::regionToFace::regionToFace
     isZone_(false),
     nearPoint_(dict.get<point>("nearPoint"))
 {
-    if (dict.readIfPresent("set", setName_))
-    {
-        isZone_ = false;
-    }
-    else
+    // A single "set" or "zone" only
+    if (!dict.readIfPresent("set", setName_))
     {
+        // Mandatory entry
         dict.readEntry("zone", setName_);
         isZone_ = true;
     }
@@ -285,7 +283,7 @@ void Foam::regionToFace::applyToSet
         }
         else
         {
-            faceSet subSet(mesh_, setName_);
+            faceSet subSet(mesh_, setName_, IOobject::NO_REGISTER);
             combine(set, true, subSet.sortedToc());
         }
     }
@@ -305,7 +303,7 @@ void Foam::regionToFace::applyToSet
         }
         else
         {
-            faceSet subSet(mesh_, setName_);
+            faceSet subSet(mesh_, setName_, IOobject::NO_REGISTER);
             combine(set, false, subSet.sortedToc());
         }
     }
diff --git a/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.H b/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.H
index f0faf5dd79..b6a21c3ddf 100644
--- a/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.H
+++ b/src/meshTools/topoSet/faceSources/regionToFace/regionToFace.H
@@ -61,7 +61,7 @@ Usage
       type       | Type name: faceSet                  | word |  yes  | -
       action     | Action applied on faces - see below | word |  yes  | -
       source     | Source name: regionToFace           | word |  yes  | -
-      set        | Name of faceSet restricting search  | word |  yes  | -
+      set / zone | Name of faceSet / zone restricting search  | word |  yes  | -
       nearPoint  | The point on/near to the region     | vector | yes | -
     \endtable
 
@@ -81,8 +81,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef regionToFace_H
-#define regionToFace_H
+#ifndef Foam_regionToFace_H
+#define Foam_regionToFace_H
 
 #include "topoSetFaceSource.H"
 #include "indirectPrimitivePatch.H"
diff --git a/src/meshTools/topoSet/faceZoneSources/cellToFaceZone/cellToFaceZone.C b/src/meshTools/topoSet/faceZoneSources/cellToFaceZone/cellToFaceZone.C
index 40e5330c36..27e103d3bd 100644
--- a/src/meshTools/topoSet/faceZoneSources/cellToFaceZone/cellToFaceZone.C
+++ b/src/meshTools/topoSet/faceZoneSources/cellToFaceZone/cellToFaceZone.C
@@ -230,7 +230,7 @@ void Foam::cellToFaceZone::applyToSet
                 else
                 {
                     // Load the sets
-                    const cellSet loadedSet(mesh_, setName);
+                    cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
                     whichCells.setMany(loadedSet.begin(), loadedSet.end());
                 }
 
@@ -276,7 +276,7 @@ void Foam::cellToFaceZone::applyToSet
                 else
                 {
                     // Load the sets
-                    const cellSet loadedSet(mesh_, setName);
+                    cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
                     whichCells.setMany(loadedSet.begin(), loadedSet.end());
                 }
                 // Select outside faces
diff --git a/src/meshTools/topoSet/faceZoneSources/setAndNormalToFaceZone/setAndNormalToFaceZone.C b/src/meshTools/topoSet/faceZoneSources/setAndNormalToFaceZone/setAndNormalToFaceZone.C
index 21e51ff5cc..7838239678 100644
--- a/src/meshTools/topoSet/faceZoneSources/setAndNormalToFaceZone/setAndNormalToFaceZone.C
+++ b/src/meshTools/topoSet/faceZoneSources/setAndNormalToFaceZone/setAndNormalToFaceZone.C
@@ -128,8 +128,8 @@ void Foam::setAndNormalToFaceZone::applyToSet
             }
 
             // Load the sets
-            faceSet loadedSet(mesh_, setName_);
-            labelHashSet& faceIds = loadedSet;
+            faceSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
+            const labelHashSet& faceLabels = loadedSet;
 
             // Start off from copy
             DynamicList<label> newAddressing(zoneSet.addressing());
@@ -138,7 +138,7 @@ void Foam::setAndNormalToFaceZone::applyToSet
             const faceList& faces = mesh_.faces();
             const pointField& points = mesh_.points();
 
-            for (const label facei : faceIds)
+            for (const label facei : faceLabels)
             {
                 if (!zoneSet.found(facei))
                 {
@@ -169,7 +169,7 @@ void Foam::setAndNormalToFaceZone::applyToSet
             }
 
             // Load the set
-            faceSet loadedSet(mesh_, setName_);
+            faceSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             // Start off empty
             DynamicList<label> newAddressing(zoneSet.addressing().size());
diff --git a/src/meshTools/topoSet/faceZoneSources/setToFaceZone/setToFaceZone.C b/src/meshTools/topoSet/faceZoneSources/setToFaceZone/setToFaceZone.C
index 7e47c0598e..02e7c50763 100644
--- a/src/meshTools/topoSet/faceZoneSources/setToFaceZone/setToFaceZone.C
+++ b/src/meshTools/topoSet/faceZoneSources/setToFaceZone/setToFaceZone.C
@@ -122,7 +122,7 @@ void Foam::setToFaceZone::applyToSet
             }
 
             // Load the sets
-            faceSet loadedSet(mesh_, setName_);
+            faceSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
             const labelHashSet& faceLabels = loadedSet;
 
             // Start off from copy
@@ -151,7 +151,7 @@ void Foam::setToFaceZone::applyToSet
             }
 
             // Load the set
-            faceSet loadedSet(mesh_, setName_);
+            faceSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             // Start off empty
             DynamicList<label> newAddressing(zoneSet.addressing().size());
diff --git a/src/meshTools/topoSet/faceZoneSources/setsToFaceZone/setsToFaceZone.C b/src/meshTools/topoSet/faceZoneSources/setsToFaceZone/setsToFaceZone.C
index ecbbb7f469..edf9a17678 100644
--- a/src/meshTools/topoSet/faceZoneSources/setsToFaceZone/setsToFaceZone.C
+++ b/src/meshTools/topoSet/faceZoneSources/setsToFaceZone/setsToFaceZone.C
@@ -135,8 +135,8 @@ void Foam::setsToFaceZone::applyToSet
             }
 
             // Load the sets
-            faceSet fSet(mesh_, faceSetName_);
-            cellSet cSet(mesh_, cellSetName_);
+            faceSet fSet(mesh_, faceSetName_, IOobject::NO_REGISTER);
+            cellSet cSet(mesh_, cellSetName_, IOobject::NO_REGISTER);
 
             // Start off from copy
             DynamicList<label> newAddressing(zoneSet.addressing());
diff --git a/src/meshTools/topoSet/pointSources/cellToPoint/cellToPoint.C b/src/meshTools/topoSet/pointSources/cellToPoint/cellToPoint.C
index e2be28d26c..4a3c58a845 100644
--- a/src/meshTools/topoSet/pointSources/cellToPoint/cellToPoint.C
+++ b/src/meshTools/topoSet/pointSources/cellToPoint/cellToPoint.C
@@ -70,7 +70,7 @@ void Foam::cellToPoint::combineImpl
     const Selector& cellLabels
 ) const
 {
-    // Add all point from cells in loadedSet
+    // Add all points from given cells
     for (const label celli : cellLabels)
     {
         const labelList& cFaces = mesh_.cells()[celli];
@@ -101,8 +101,7 @@ void Foam::cellToPoint::combine
     else
     {
         // Load the set
-        cellSet loadedSet(mesh_, setName);
-
+        cellSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& cellLabels = loadedSet;
 
         combineImpl(set, add, cellLabels);
diff --git a/src/meshTools/topoSet/pointSources/faceToPoint/faceToPoint.C b/src/meshTools/topoSet/pointSources/faceToPoint/faceToPoint.C
index aac6b62161..cd2212dcbe 100644
--- a/src/meshTools/topoSet/pointSources/faceToPoint/faceToPoint.C
+++ b/src/meshTools/topoSet/pointSources/faceToPoint/faceToPoint.C
@@ -72,7 +72,7 @@ void Foam::faceToPoint::combine
     {
         const auto& faceLabels = mesh_.faceZones()[setName].addressing();
 
-        // Add all points from faces in loadedSet
+        // Add all points from given faces
         for (const label facei : faceLabels)
         {
             const face& f = mesh_.faces()[facei];
@@ -83,10 +83,10 @@ void Foam::faceToPoint::combine
     else
     {
         // Load the set
-        faceSet loadedSet(mesh_, setName);
+        faceSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
         const labelHashSet& faceLabels = loadedSet;
 
-        // Add all points from faces in loadedSet
+        // Add all points from given faces
         for (const label facei : faceLabels)
         {
             const face& f = mesh_.faces()[facei];
diff --git a/src/meshTools/topoSet/pointSources/pointToPoint/pointToPoint.C b/src/meshTools/topoSet/pointSources/pointToPoint/pointToPoint.C
index 0f428972cc..12b379a790 100644
--- a/src/meshTools/topoSet/pointSources/pointToPoint/pointToPoint.C
+++ b/src/meshTools/topoSet/pointSources/pointToPoint/pointToPoint.C
@@ -114,7 +114,7 @@ void Foam::pointToPoint::applyToSet
             }
             else
             {
-                pointSet loadedSet(mesh_, setName);
+                pointSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
 
                 set.addSet(loadedSet);
             }
@@ -137,7 +137,7 @@ void Foam::pointToPoint::applyToSet
             }
             else
             {
-                pointSet loadedSet(mesh_, setName);
+                pointSet loadedSet(mesh_, setName, IOobject::NO_REGISTER);
 
                 set.subtractSet(loadedSet);
             }
diff --git a/src/meshTools/topoSet/pointZoneSources/setToPointZone/setToPointZone.C b/src/meshTools/topoSet/pointZoneSources/setToPointZone/setToPointZone.C
index 40e50aa54f..e2cd75d796 100644
--- a/src/meshTools/topoSet/pointZoneSources/setToPointZone/setToPointZone.C
+++ b/src/meshTools/topoSet/pointZoneSources/setToPointZone/setToPointZone.C
@@ -114,7 +114,7 @@ void Foam::setToPointZone::applyToSet
             }
 
             // Load the set
-            pointSet loadedSet(mesh_, setName_);
+            pointSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
             const labelHashSet& pointLabels = loadedSet;
 
             // Start off from copy
@@ -140,7 +140,7 @@ void Foam::setToPointZone::applyToSet
             }
 
             // Load the set
-            pointSet loadedSet(mesh_, setName_);
+            pointSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
 
             // Start off empty
             DynamicList<label> newAddressing(zoneSet.addressing().size());
diff --git a/src/meshTools/topoSet/topoSets/cellBitSet.C b/src/meshTools/topoSet/topoSets/cellBitSet.C
index a830359ea0..f9fc15988d 100644
--- a/src/meshTools/topoSet/topoSets/cellBitSet.C
+++ b/src/meshTools/topoSet/topoSets/cellBitSet.C
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018-2022 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -34,18 +34,12 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(cellBitSet, 0);
+    defineTypeName(cellBitSet);
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::cellBitSet::cellBitSet(const polyMesh& mesh)
-:
-    cellBitSet(mesh, false)
-{}
-
-
 Foam::cellBitSet::cellBitSet(const polyMesh& mesh, const bool val)
 :
     topoBitSet(mesh, "cellBitSet", mesh.nCells(), val)
diff --git a/src/meshTools/topoSet/topoSets/cellBitSet.H b/src/meshTools/topoSet/topoSets/cellBitSet.H
index 98d803e81b..278370a8d5 100644
--- a/src/meshTools/topoSet/topoSets/cellBitSet.H
+++ b/src/meshTools/topoSet/topoSets/cellBitSet.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018-2022 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -96,16 +96,14 @@ class cellBitSet
 public:
 
     //- Runtime type information
-    TypeName("cellBitSet");
+    TypeNameNoDebug("cellBitSet");
 
 
     // Constructors
 
-        //- Construct with nCells elements, all elements unset
-        explicit cellBitSet(const polyMesh& mesh);
-
-        //- Construct with nCells elements, using initial val
-        cellBitSet(const polyMesh& mesh, const bool val);
+        //- Construct with nCells elements,
+        //- all elements unset or initial value
+        explicit cellBitSet(const polyMesh& mesh, const bool val = false);
 
         //- Copy construct from bitset, resizing to nCells elements as required
         cellBitSet(const polyMesh& mesh, const bitSet& bits);
diff --git a/src/meshTools/topoSet/topoSets/cellSet.C b/src/meshTools/topoSet/topoSets/cellSet.C
index 7df945566e..2cfd0b7dc0 100644
--- a/src/meshTools/topoSet/topoSets/cellSet.C
+++ b/src/meshTools/topoSet/topoSets/cellSet.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,11 +37,10 @@ License
 
 namespace Foam
 {
-defineTypeNameAndDebug(cellSet, 0);
-
-addToRunTimeSelectionTable(topoSet, cellSet, word);
-addToRunTimeSelectionTable(topoSet, cellSet, size);
-addToRunTimeSelectionTable(topoSet, cellSet, set);
+    defineTypeName(cellSet);
+    addToRunTimeSelectionTable(topoSet, cellSet, word);
+    addToRunTimeSelectionTable(topoSet, cellSet, size);
+    addToRunTimeSelectionTable(topoSet, cellSet, set);
 }
 
 
@@ -53,18 +52,24 @@ Foam::cellSet::cellSet(const IOobject& io)
 {}
 
 
+Foam::cellSet::cellSet(const IOobject& io, const Foam::zero)
+:
+    topoSet(io, Foam::zero{})
+{}
+
+
 Foam::cellSet::cellSet
 (
     const polyMesh& mesh,
     const word& name,
     IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
 )
 :
-    topoSet(mesh, typeName, name, rOpt, wOpt)
+    topoSet(mesh, typeName, name, rOpt, wOpt, reg)
 {
-    // Make sure set within valid range
-    check(mesh.nCells());
+    check(mesh.nCells());  // Valid range?
 }
 
 
@@ -72,11 +77,11 @@ Foam::cellSet::cellSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    topoSet(mesh, name, size, wOpt)
+    topoSet(mesh, name, initialCapacity, wOpt)
 {}
 
 
@@ -149,14 +154,14 @@ Foam::cellSet::cellSet
 (
     const Time& runTime,
     const word& name,
-    const label size,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
     topoSet
     (
         findIOobject(runTime, name, IOobject::NO_READ, wOpt),
-        size
+        initialCapacity
     )
 {}
 
@@ -177,6 +182,28 @@ Foam::cellSet::cellSet
 {}
 
 
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+Foam::labelHashSet Foam::cellSet::readContents
+(
+    const polyMesh& mesh,
+    const word& name
+)
+{
+    cellSet reader
+    (
+        topoSet::findIOobject(mesh, name, IOobjectOption::NO_REGISTER),
+        Foam::zero{}
+    );
+
+    labelHashSet labels;
+    reader.readIOcontents(typeName, labels);
+    reader.checkLabels(labels, mesh.nCells());  // Valid range?
+
+    return labels;
+}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 Foam::label Foam::cellSet::maxSize(const polyMesh& mesh) const
diff --git a/src/meshTools/topoSet/topoSets/cellSet.H b/src/meshTools/topoSet/topoSets/cellSet.H
index b678b047b0..820e2b938c 100644
--- a/src/meshTools/topoSet/topoSets/cellSet.H
+++ b/src/meshTools/topoSet/topoSets/cellSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -62,7 +62,7 @@ class cellSet
 public:
 
     //- Runtime type information
-    TypeName("cellSet");
+    TypeNameNoDebug("cellSet");
 
 
     // Constructors
@@ -70,25 +70,43 @@ public:
         //- Construct from IOobject. No checking.
         explicit cellSet(const IOobject& io);
 
-        //- Construct from polyMesh and name. Checks for valid cell ids.
+        //- Construct empty (no-read) with IOobject information
+        cellSet(const IOobject& io, const Foam::zero);
+
+        //- Construct from polyMesh (registry) and name.
+        //- Checks for valid cell ids.
         cellSet
         (
             const polyMesh& mesh,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct empty with initial size for labelHashSet
+        //- Construct from polyMesh (registry), name and registration option
         cellSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            IOobjectOption::registerOption reg,
+            IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        )
+        :
+            cellSet(mesh, name, rOpt, wOpt, reg)
+        {}
+
+        //- Construct empty (no-read) with initial labelHashSet capacity
+        cellSet
+        (
+            const polyMesh& mesh,
+            const word& name,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct from existing set
+        //- Copy construct (no-read) from existing set
         cellSet
         (
             const polyMesh& mesh,
@@ -97,7 +115,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy of labelHashSet
+        //- Copy construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         cellSet
         (
             const polyMesh& mesh,
@@ -106,7 +125,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with moving labelHashSet
+        //- Move construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         cellSet
         (
             const polyMesh& mesh,
@@ -115,7 +135,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy labels
+        //- Copy construct (no-read) from labels,
+        //- with search for IOobject instance.
         cellSet
         (
             const polyMesh& mesh,
@@ -125,34 +146,46 @@ public:
         );
 
 
-        // Used for tetMesh cellSet only.
+        //- Construct from objectRegistry and name.
+        //- Used for tetMesh cellSet only.
+        cellSet
+        (
+            const Time&,
+            const word& name,
+            IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        );
 
-            //- Construct from objectRegistry and name.
-            cellSet
-            (
-                const Time&,
-                const word& name,
-                IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-                IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
-            );
+        //- Construct empty (no-read) with initial labelHashSet capacity
+        //- from objectRegistry.
+        //- Used for tetMesh cellSet only.
+        cellSet
+        (
+            const Time&,
+            const word& name,
+            const label initialCapacity,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        );
 
-            //- Construct empty from objectRegistry.
-            cellSet
-            (
-                const Time&,
-                const word& name,
-                const label size,
-                IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
-            );
+        //- Copy construct (no-read) from labelHashSet.
+        //- Used for tetMesh cellSet only.
+        cellSet
+        (
+            const Time&,
+            const word& name,
+            const labelHashSet& labels,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        );
 
-            //- Construct from labelHashSet
-            cellSet
-            (
-                const Time&,
-                const word& name,
-                const labelHashSet& labels,
-                IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
-            );
+
+    // Factory Methods
+
+        //- Read and return contents. Intermediate IOobject is not registered
+        static labelHashSet readContents
+        (
+            const polyMesh& mesh,
+            const word& name
+        );
 
 
     //- Destructor
diff --git a/src/meshTools/topoSet/topoSets/cellZoneSet.C b/src/meshTools/topoSet/topoSets/cellZoneSet.C
index fd36af0d2f..af461fb6a2 100644
--- a/src/meshTools/topoSet/topoSets/cellZoneSet.C
+++ b/src/meshTools/topoSet/topoSets/cellZoneSet.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2022,2024 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -36,18 +36,18 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(cellZoneSet, 0);
+    defineTypeName(cellZoneSet);
     addToRunTimeSelectionTable(topoSet, cellZoneSet, word);
     addToRunTimeSelectionTable(topoSet, cellZoneSet, size);
     addToRunTimeSelectionTable(topoSet, cellZoneSet, set);
 }
 
+
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
 void Foam::cellZoneSet::updateSet()
 {
-    labelList order(sortedOrder(addressing_));
-    inplaceReorder(order, addressing_);
+    Foam::sort(addressing_);
 
     cellSet::clearStorage();
     cellSet::reserve(addressing_.size());
@@ -61,46 +61,46 @@ Foam::cellZoneSet::cellZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    IOobjectOption::readOption rOpt,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    cellSet(mesh, name, 1024),  // do not read cellSet
-    mesh_(mesh),
-    addressing_()
-{
-    const cellZoneMesh& cellZones = mesh.cellZones();
-    label zoneID = cellZones.findZoneID(name);
-
-    if
-    (
-         IOobjectOption::isReadRequired(rOpt)
-     || (IOobjectOption::isReadOptional(rOpt) && zoneID != -1)
-    )
-    {
-        const cellZone& fz = cellZones[zoneID];
-        addressing_ = fz;
-    }
-
-    updateSet();
-
-    check(mesh.nCells());
-}
+    cellSet(mesh, name, initialCapacity, wOpt),  // Construct no-read
+    mesh_(mesh)
+{}
 
 
 Foam::cellZoneSet::cellZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    IOobjectOption::readOption rOpt,
     IOobjectOption::writeOption wOpt
 )
 :
-    cellSet(mesh, name, size, wOpt),
-    mesh_(mesh),
-    addressing_()
+    cellZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto& zones = mesh.cellZones();
+    const auto* zonePtr = zones.cfindZone(name);
+
+    if (!zonePtr)
+    {
+        if (IOobjectOption::isReadRequired(rOpt))
+        {
+            FatalErrorInFunction
+                << "Zone named " << name << " not found.  "
+                << "List of available zone names: " << zones.names() << nl
+                << exit(FatalError);
+        }
+    }
+    else if (IOobjectOption::isAnyRead(rOpt))
+    {
+        const auto& zn = *zonePtr;
+        addressing_ = zn;
+    }
+
     updateSet();
+    check(mesh.nCells());
 }
 
 
@@ -112,15 +112,19 @@ Foam::cellZoneSet::cellZoneSet
     IOobjectOption::writeOption wOpt
 )
 :
-    cellSet(mesh, name, set.size(), wOpt),
-    mesh_(mesh),
-    addressing_
-    (
-        isA<const cellZoneSet>(set)
-      ? refCast<const cellZoneSet>(set).addressing()
-      : set.sortedToc()
-    )
+    cellZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto* zonePtr = isA<cellZoneSet>(set);
+
+    if (zonePtr)
+    {
+        addressing_ = zonePtr->addressing();
+    }
+    else
+    {
+        addressing_ = set.sortedToc();
+    }
+
     updateSet();
 }
 
@@ -141,7 +145,7 @@ void Foam::cellZoneSet::invert(const label maxLen)
     }
 
     // Fill
-    addressing_.setSize(n);
+    addressing_.resize_nocopy(n);
     n = 0;
 
     for (label celli = 0; celli < maxLen; ++celli)
@@ -157,31 +161,15 @@ void Foam::cellZoneSet::invert(const label maxLen)
 }
 
 
-void Foam::cellZoneSet::subset(const topoSet& set)
+void Foam::cellZoneSet::subset(const labelUList& elems)
 {
     DynamicList<label> newAddressing(addressing_.size());
 
-    const auto* setPtr = dynamic_cast<const cellZoneSet*>(&set);
-
-    if (setPtr)
+    for (const label id : elems)
     {
-        for (const label celli : setPtr->addressing())
+        if (found(id))
         {
-            if (found(celli))
-            {
-                newAddressing.append(celli);
-            }
-        }
-    }
-    else
-    {
-        // Assume a cellSet
-        for (const label celli : refCast<const cellSet>(set).sortedToc())
-        {
-            if (found(celli))
-            {
-                newAddressing.append(celli);
-            }
+            newAddressing.push_back(id);
         }
     }
 
@@ -190,15 +178,32 @@ void Foam::cellZoneSet::subset(const topoSet& set)
 }
 
 
-void Foam::cellZoneSet::subset(const labelUList& set)
+void Foam::cellZoneSet::subset(const topoSet& set)
 {
-    DynamicList<label> newAddressing(addressing_.size());
+    const auto* zonePtr = isA<cellZoneSet>(set);
 
-    for (const label celli : set)
+    if (zonePtr)
     {
-        if (found(celli))
+        // Is a cellZoneSet
+        this->subset(zonePtr->addressing());
+    }
+    else
+    {
+        // Assume a cellSet
+        this->subset(refCast<const cellSet>(set).sortedToc());
+    }
+}
+
+
+void Foam::cellZoneSet::addSet(const labelUList& elems)
+{
+    DynamicList<label> newAddressing(addressing_);
+
+    for (const label id : elems)
+    {
+        if (!found(id))
         {
-            newAddressing.append(celli);
+            newAddressing.push_back(id);
         }
     }
 
@@ -209,46 +214,33 @@ void Foam::cellZoneSet::subset(const labelUList& set)
 
 void Foam::cellZoneSet::addSet(const topoSet& set)
 {
-    DynamicList<label> newAddressing(addressing_);
+    const auto* zonePtr = isA<cellZoneSet>(set);
 
-    const auto* setPtr = dynamic_cast<const cellZoneSet*>(&set);
-
-    if (setPtr)
+    if (zonePtr)
     {
-        for (const label celli : setPtr->addressing())
-        {
-            if (!found(celli))
-            {
-                newAddressing.append(celli);
-            }
-        }
+        // Is a cellZoneSet
+        this->addSet(zonePtr->addressing());
     }
     else
     {
         // Assume a cellSet
-        for (const label celli : refCast<const cellSet>(set).sortedToc())
-        {
-            if (!found(celli))
-            {
-                newAddressing.append(celli);
-            }
-        }
+        this->addSet(refCast<const cellSet>(set).sortedToc());
     }
-
-    addressing_.transfer(newAddressing);
-    updateSet();
 }
 
 
-void Foam::cellZoneSet::addSet(const labelUList& set)
+void Foam::cellZoneSet::subtractSet(const labelUList& elems)
 {
-    DynamicList<label> newAddressing(addressing_);
+    DynamicList<label> newAddressing(addressing_.size());
 
-    for (const label celli : set)
+    const labelHashSet set(elems);
+
+    for (const label id : addressing_)
     {
-        if (!found(celli))
+        if (!set.found(id))
         {
-            newAddressing.append(celli);
+            // Retain if not in the topoSet (parameter)
+            newAddressing.push_back(id);
         }
     }
 
@@ -261,32 +253,12 @@ void Foam::cellZoneSet::subtractSet(const topoSet& set)
 {
     DynamicList<label> newAddressing(addressing_.size());
 
-    for (const label celli : addressing_)
+    for (const label id : addressing_)
     {
-        if (!set.found(celli))
+        if (!set.found(id))
         {
             // Not found in zoneSet so add
-            newAddressing.append(celli);
-        }
-    }
-
-    addressing_.transfer(newAddressing);
-    updateSet();
-}
-
-
-void Foam::cellZoneSet::subtractSet(const labelUList& elems)
-{
-    DynamicList<label> newAddressing(addressing_.size());
-
-    const labelHashSet zoneSet(elems);
-
-    for (const label celli : addressing_)
-    {
-        if (!zoneSet.found(celli))
-        {
-            // Not found in zoneSet so add
-            newAddressing.append(celli);
+            newAddressing.push_back(id);
         }
     }
 
@@ -318,56 +290,49 @@ bool Foam::cellZoneSet::writeObject
 ) const
 {
     // Write shadow cellSet
-    word oldTypeName = typeName;
+    const word oldTypeName = typeName;
     const_cast<word&>(type()) = cellSet::typeName;
     bool ok = cellSet::writeObject(streamOpt, writeOnProc);
     const_cast<word&>(type()) = oldTypeName;
 
     // Modify cellZone
-    cellZoneMesh& cellZones = const_cast<polyMesh&>(mesh_).cellZones();
-    label zoneID = cellZones.findZoneID(name());
+    auto& zones = const_cast<polyMesh&>(mesh_).cellZones();
+    auto* zonePtr = zones.findZone(name());
 
-    if (zoneID == -1)
+    if (zonePtr)
     {
-        zoneID = cellZones.size();
-
-        cellZones.emplace_back
-        (
-            name(),
-            addressing_,
-            zoneID,
-            cellZones
-        );
+        zonePtr->resetAddressing(addressing_);
     }
     else
     {
-        cellZones[zoneID] = addressing_;
+        zones.emplace_back
+        (
+            name(),
+            addressing_,
+            zones.size(),  // zoneID
+            zones
+        );
     }
-    cellZones.clearAddressing();
+    zones.clearAddressing();
 
-    return ok && cellZones.write(writeOnProc);
+    return ok && zones.write(writeOnProc);
 }
 
 
 void Foam::cellZoneSet::updateMesh(const mapPolyMesh& morphMap)
 {
-    // cellZone
-    labelList newAddressing(addressing_.size());
+    DynamicList<label> newAddressing(addressing_.size());
 
-    label n = 0;
     for (const label celli : addressing_)
     {
         label newCelli = morphMap.reverseCellMap()[celli];
         if (newCelli >= 0)
         {
-            newAddressing[n] = newCelli;
-            ++n;
+            newAddressing.push_back(newCelli);
         }
     }
-    newAddressing.resize(n);
 
     addressing_.transfer(newAddressing);
-
     updateSet();
 }
 
diff --git a/src/meshTools/topoSet/topoSets/cellZoneSet.H b/src/meshTools/topoSet/topoSets/cellZoneSet.H
index cb53106b80..015e09b6f2 100644
--- a/src/meshTools/topoSet/topoSets/cellZoneSet.H
+++ b/src/meshTools/topoSet/topoSets/cellZoneSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2022 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -62,7 +62,7 @@ class cellZoneSet
 public:
 
     //- Runtime type information
-    TypeName("cellZoneSet");
+    TypeNameNoDebug("cellZoneSet");
 
 
     // Constructors
@@ -76,16 +76,16 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct from initial size for labelHashSet
+        //- Construct empty (no-read) with initial labelHashSet capacity.
         cellZoneSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Copy construct from existing set
+        //- Copy construct (no-read) from existing set
         cellZoneSet
         (
             const polyMesh& mesh,
@@ -102,16 +102,17 @@ public:
 
     // Member functions
 
-        const labelList& addressing() const
+        const labelList& addressing() const noexcept
         {
             return addressing_;
         }
 
-        labelList& addressing()
+        labelList& addressing() noexcept
         {
             return addressing_;
         }
 
+
         //- Sort addressing and make cellSet part consistent with addressing
         void updateSet();
 
@@ -119,26 +120,24 @@ public:
         //  Insert all members [0,maxLen) which were not in set
         virtual void invert(const label maxLen);
 
+        //- Subset contents. Only elements present in both sets remain.
+        virtual void subset(const labelUList& elems);
+
         //- Subset contents. Only elements present in both sets remain.
         virtual void subset(const topoSet& set);
 
-        //- Add elements present in set.
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Subtract elements present in set.
+        //- Subtract given elements from the set
+        virtual void subtractSet(const labelUList& elems);
+
+        //- Subtract given elements from the set
         virtual void subtractSet(const topoSet& set);
 
-        // Variants taking labelUList&
-
-            //- Subset contents. Only elements present in both sets remain.
-            virtual void subset(const labelUList& set);
-
-            //- Add elements present in set.
-            virtual void addSet(const labelUList& set);
-
-            //- Subtract elements present in set.
-            virtual void subtractSet(const labelUList& set);
-
         //- Sync cellSet across coupled patches; update cellZone from cellSet
         virtual void sync(const polyMesh& mesh);
 
diff --git a/src/meshTools/topoSet/topoSets/faceBitSet.C b/src/meshTools/topoSet/topoSets/faceBitSet.C
index cb1fe1e729..9633fb9955 100644
--- a/src/meshTools/topoSet/topoSets/faceBitSet.C
+++ b/src/meshTools/topoSet/topoSets/faceBitSet.C
@@ -35,18 +35,12 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(faceBitSet, 0);
+    defineTypeName(faceBitSet);
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::faceBitSet::faceBitSet(const polyMesh& mesh)
-:
-    faceBitSet(mesh, false)
-{}
-
-
 Foam::faceBitSet::faceBitSet(const polyMesh& mesh, const bool val)
 :
     topoBitSet(mesh, "faceBitSet", mesh.nFaces(), val)
diff --git a/src/meshTools/topoSet/topoSets/faceBitSet.H b/src/meshTools/topoSet/topoSets/faceBitSet.H
index ca53dca980..b9185a2073 100644
--- a/src/meshTools/topoSet/topoSets/faceBitSet.H
+++ b/src/meshTools/topoSet/topoSets/faceBitSet.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -56,16 +56,14 @@ class faceBitSet
 public:
 
     //- Runtime type information
-    TypeName("faceBitSet");
+    TypeNameNoDebug("faceBitSet");
 
 
     // Constructors
 
-        //- Construct with nFaces elements, all elements unset
-        explicit faceBitSet(const polyMesh& mesh);
-
-        //- Construct with nFaces elements, using initial val
-        faceBitSet(const polyMesh& mesh, const bool val);
+        //- Construct with nFaces elements,
+        //- all elements unset or initial value
+        explicit faceBitSet(const polyMesh& mesh, const bool val = false);
 
         //- Copy construct from bitset, resizing to nFaces elements as required
         faceBitSet(const polyMesh& mesh, const bitSet& bits);
diff --git a/src/meshTools/topoSet/topoSets/faceBoolSet.C b/src/meshTools/topoSet/topoSets/faceBoolSet.C
index 0f6e1c99a5..ebfc695760 100644
--- a/src/meshTools/topoSet/topoSets/faceBoolSet.C
+++ b/src/meshTools/topoSet/topoSets/faceBoolSet.C
@@ -35,7 +35,7 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(faceBoolSet, 0);
+    defineTypeName(faceBoolSet);
 }
 
 
diff --git a/src/meshTools/topoSet/topoSets/faceBoolSet.H b/src/meshTools/topoSet/topoSets/faceBoolSet.H
index 2745221ca3..fd2fc89b96 100644
--- a/src/meshTools/topoSet/topoSets/faceBoolSet.H
+++ b/src/meshTools/topoSet/topoSets/faceBoolSet.H
@@ -56,7 +56,7 @@ class faceBoolSet
 public:
 
     //- Runtime type information
-    TypeName("faceBoolSet");
+    TypeNameNoDebug("faceBoolSet");
 
 
     // Constructors
diff --git a/src/meshTools/topoSet/topoSets/faceSet.C b/src/meshTools/topoSet/topoSets/faceSet.C
index 1a87e4f9b7..ad5296b2ef 100644
--- a/src/meshTools/topoSet/topoSets/faceSet.C
+++ b/src/meshTools/topoSet/topoSets/faceSet.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,7 +37,7 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(faceSet, 0);
+    defineTypeName(faceSet);
     addToRunTimeSelectionTable(topoSet, faceSet, word);
     addToRunTimeSelectionTable(topoSet, faceSet, size);
     addToRunTimeSelectionTable(topoSet, faceSet, set);
@@ -51,17 +51,24 @@ Foam::faceSet::faceSet(const IOobject& io)
 {}
 
 
+Foam::faceSet::faceSet(const IOobject& io, const Foam::zero)
+:
+    topoSet(io, Foam::zero{})
+{}
+
+
 Foam::faceSet::faceSet
 (
     const polyMesh& mesh,
     const word& name,
     IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
 )
 :
-    topoSet(mesh, typeName, name, rOpt, wOpt)
+    topoSet(mesh, typeName, name, rOpt, wOpt, reg)
 {
-    check(mesh.nFaces());
+    check(mesh.nFaces());  // Valid range?
 }
 
 
@@ -69,11 +76,11 @@ Foam::faceSet::faceSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    topoSet(mesh, name, size, wOpt)
+    topoSet(mesh, name, initialCapacity, wOpt)
 {}
 
 
@@ -125,6 +132,28 @@ Foam::faceSet::faceSet
 {}
 
 
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+Foam::labelHashSet Foam::faceSet::readContents
+(
+    const polyMesh& mesh,
+    const word& name
+)
+{
+    faceSet reader
+    (
+        topoSet::findIOobject(mesh, name, IOobjectOption::NO_REGISTER),
+        Foam::zero{}
+    );
+
+    labelHashSet labels;
+    reader.readIOcontents(typeName, labels);
+    reader.checkLabels(labels, mesh.nFaces());  // Valid range?
+
+    return labels;
+}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 void Foam::faceSet::sync(const polyMesh& mesh)
diff --git a/src/meshTools/topoSet/topoSets/faceSet.H b/src/meshTools/topoSet/topoSets/faceSet.H
index 02f6e940e8..13dda382aa 100644
--- a/src/meshTools/topoSet/topoSets/faceSet.H
+++ b/src/meshTools/topoSet/topoSets/faceSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -56,33 +56,50 @@ class faceSet
 public:
 
     //- Runtime type information
-    TypeName("faceSet");
+    TypeNameNoDebug("faceSet");
 
 
     // Constructors
 
-        //- Construct from IOobject
+        //- Construct from IOobject. No checking.
         explicit faceSet(const IOobject& io);
 
-        //- Construct from objectRegistry and name
+        //- Construct empty (no-read) with IOobject information
+        faceSet(const IOobject& io, const Foam::zero);
+
+        //- Construct from polyMesh (registry) and name
         faceSet
         (
             const polyMesh& mesh,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct empty with initial size for labelHashSet
+        //- Construct from polyMesh (registry), name and registration option
         faceSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            IOobjectOption::registerOption reg,
+            IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        )
+        :
+            faceSet(mesh, name, rOpt, wOpt, reg)
+        {}
+
+        //- Construct empty (no-read) with initial labelHashSet capacity.
+        faceSet
+        (
+            const polyMesh& mesh,
+            const word& name,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct from existing set
+        //- Copy construct (no-read) from existing set
         faceSet
         (
             const polyMesh& mesh,
@@ -91,7 +108,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy of labelHashSet
+        //- Copy construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         faceSet
         (
             const polyMesh& mesh,
@@ -100,7 +118,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with moving labelHashSet
+        //- Move construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         faceSet
         (
             const polyMesh& mesh,
@@ -109,7 +128,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy of labels
+        //- Copy construct (no-read) from labels,
+        //- with search for IOobject instance.
         faceSet
         (
             const polyMesh& mesh,
@@ -119,6 +139,16 @@ public:
         );
 
 
+    // Factory Methods
+
+        //- Read and return contents. Intermediate IOobject is not registered
+        static labelHashSet readContents
+        (
+            const polyMesh& mesh,
+            const word& name
+        );
+
+
     //- Destructor
     virtual ~faceSet() = default;
 
diff --git a/src/meshTools/topoSet/topoSets/faceZoneSet.C b/src/meshTools/topoSet/topoSets/faceZoneSet.C
index 73431e3890..051aa0506b 100644
--- a/src/meshTools/topoSet/topoSets/faceZoneSet.C
+++ b/src/meshTools/topoSet/topoSets/faceZoneSet.C
@@ -40,7 +40,7 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(faceZoneSet, 0);
+    defineTypeName(faceZoneSet);
     addToRunTimeSelectionTable(topoSet, faceZoneSet, word);
     addToRunTimeSelectionTable(topoSet, faceZoneSet, size);
     addToRunTimeSelectionTable(topoSet, faceZoneSet, set);
@@ -51,9 +51,18 @@ namespace Foam
 
 void Foam::faceZoneSet::updateSet()
 {
-    labelList order(sortedOrder(addressing_));
-    addressing_ = labelUIndList(addressing_, order)();
-    flipMap_ = boolUIndList(flipMap_, order)();
+    if (flipMap_.size() == addressing_.size())
+    {
+        labelList order(Foam::sortedOrder(addressing_));
+        addressing_ = labelUIndList(addressing_, order)();
+        flipMap_ = boolUIndList(flipMap_, order)();
+    }
+    else
+    {
+        Foam::sort(addressing_);
+        flipMap_.resize_nocopy(addressing_.size());
+        flipMap_ = false;
+    }
 
     faceSet::clearStorage();
     faceSet::reserve(addressing_.size());
@@ -67,57 +76,47 @@ Foam::faceZoneSet::faceZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    IOobjectOption::readOption rOpt,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    faceSet(mesh, name, 1024),  // do not read faceSet
-    mesh_(mesh),
-    addressing_(),
-    flipMap_()
-{
-    const faceZoneMesh& faceZones = mesh.faceZones();
-    label zoneID = faceZones.findZoneID(name);
-
-    if (IOobjectOption::isReadRequired(rOpt) && zoneID == -1)
-    {
-        FatalErrorInFunction
-            << "Zone named " << name << " not found.  "
-            << "List of available zone names: " << faceZones.names()
-            << exit(FatalError);
-    }
-
-    if
-    (
-         IOobjectOption::isReadRequired(rOpt)
-     || (IOobjectOption::isReadOptional(rOpt) && zoneID != -1)
-    )
-    {
-        const faceZone& fz = faceZones[zoneID];
-        addressing_ = fz.addressing();
-        flipMap_ = fz.flipMap();
-    }
-
-    updateSet();
-
-    check(mesh.nFaces());
-}
+    faceSet(mesh, name, initialCapacity, wOpt),  // Construct no-read
+    mesh_(mesh)
+{}
 
 
 Foam::faceZoneSet::faceZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    IOobjectOption::readOption rOpt,
     IOobjectOption::writeOption wOpt
 )
 :
-    faceSet(mesh, name, size, wOpt),
-    mesh_(mesh),
-    addressing_(),
-    flipMap_()
+    faceZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto& zones = mesh.faceZones();
+    const auto* zonePtr = zones.cfindZone(name);
+
+    if (!zonePtr)
+    {
+        if (IOobjectOption::isReadRequired(rOpt))
+        {
+            FatalErrorInFunction
+                << "Zone named " << name << " not found.  "
+                << "List of available zone names: " << zones.names() << nl
+                << exit(FatalError);
+        }
+    }
+    else if (IOobjectOption::isAnyRead(rOpt))
+    {
+        const auto& zn = *zonePtr;
+        addressing_ = zn.addressing();
+        flipMap_ = zn.flipMap();
+    }
+
     updateSet();
+    check(mesh.nFaces());
 }
 
 
@@ -129,11 +128,21 @@ Foam::faceZoneSet::faceZoneSet
     IOobjectOption::writeOption wOpt
 )
 :
-    faceSet(mesh, name, set.size(), wOpt),
-    mesh_(mesh),
-    addressing_(refCast<const faceZoneSet>(set).addressing()),
-    flipMap_(refCast<const faceZoneSet>(set).flipMap())
+    faceZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto* zonePtr = isA<faceZoneSet>(set);
+
+    if (zonePtr)
+    {
+        addressing_ = zonePtr->addressing();
+        flipMap_ = zonePtr->flipMap();
+    }
+    else
+    {
+        // No flipMap for faceSet - handled in updateSet()
+        addressing_ = set.sortedToc();
+    }
+
     updateSet();
 }
 
@@ -145,24 +154,24 @@ void Foam::faceZoneSet::invert(const label maxLen)
     // Count
     label n = 0;
 
-    for (label facei = 0; facei < maxLen; ++facei)
+    for (label id = 0; id < maxLen; ++id)
     {
-        if (!found(facei))
+        if (!topoSet::contains(id))
         {
             ++n;
         }
     }
 
     // Fill
-    addressing_.setSize(n);
-    flipMap_.setSize(n);
+    addressing_.resize_nocopy(n);
+    flipMap_.resize_nocopy(n);
     n = 0;
 
-    for (label facei = 0; facei < maxLen; ++facei)
+    for (label id = 0; id < maxLen; ++id)
     {
-        if (!found(facei))
+        if (!topoSet::contains(id))
         {
-            addressing_[n] = facei;
+            addressing_[n] = id;
             flipMap_[n] = false;         //? or true?
             ++n;
         }
@@ -204,7 +213,7 @@ void Foam::faceZoneSet::subset
         }
     }
 
-    if (nConflict > 0)
+    if (nConflict)
     {
         WarningInFunction
             << "subset : there are " << nConflict
@@ -220,24 +229,28 @@ void Foam::faceZoneSet::subset
 
 void Foam::faceZoneSet::subset(const topoSet& set)
 {
-    const auto* setPtr = dynamic_cast<const faceZoneSet*>(&set);
+    const auto* zonePtr = isA<faceZoneSet>(set);
 
-    if (setPtr)
+    if (zonePtr)
     {
-        subset(setPtr->name(), setPtr->addressing(), setPtr->flipMap());
+        subset(zonePtr->name(), zonePtr->addressing(), zonePtr->flipMap());
     }
     else
     {
         // Assume a faceSet. Ignore flipMap
-        const auto& fSet = refCast<const faceSet>(set);
-        subset(fSet.name(), fSet.sortedToc(), boolList::null());
+        subset
+        (
+            set.name(),
+            refCast<const faceSet>(set).sortedToc(),
+            boolList::null()
+        );
     }
 }
 
 
-void Foam::faceZoneSet::subset(const labelUList& set)
+void Foam::faceZoneSet::subset(const labelUList& elems)
 {
-    subset(word::null, set, boolList::null());
+    subset(word::null, elems, boolList::null());
 }
 
 
@@ -292,24 +305,28 @@ void Foam::faceZoneSet::addSet
 
 void Foam::faceZoneSet::addSet(const topoSet& set)
 {
-    const auto* setPtr = dynamic_cast<const faceZoneSet*>(&set);
+    const auto* zonePtr = isA<faceZoneSet>(set);
 
-    if (setPtr)
+    if (zonePtr)
     {
-        addSet(setPtr->name(), setPtr->addressing(), setPtr->flipMap());
+        addSet(zonePtr->name(), zonePtr->addressing(), zonePtr->flipMap());
     }
     else
     {
         // Assume a faceSet. Ignore flipMap
-        const auto& fSet = refCast<const faceSet>(set);
-        addSet(fSet.name(), fSet.sortedToc(), boolList::null());
+        addSet
+        (
+            set.name(),
+            refCast<const faceSet>(set).sortedToc(),
+            boolList::null()
+        );
     }
 }
 
 
-void Foam::faceZoneSet::addSet(const labelUList& set)
+void Foam::faceZoneSet::addSet(const labelUList& elems)
 {
-    addSet(word::null, set, boolList::null());
+    addSet(word::null, elems, boolList::null());
 }
 
 
@@ -366,24 +383,28 @@ void Foam::faceZoneSet::subtractSet
 
 void Foam::faceZoneSet::subtractSet(const topoSet& set)
 {
-    const auto* setPtr = dynamic_cast<const faceZoneSet*>(&set);
+    const auto* zonePtr = isA<faceZoneSet>(set);
 
-    if (setPtr)
+    if (zonePtr)
     {
-        subtractSet(setPtr->name(), setPtr->addressing(), setPtr->flipMap());
+        subtractSet(zonePtr->name(), zonePtr->addressing(), zonePtr->flipMap());
     }
     else
     {
         // Assume a faceSet. Ignore flipMap
-        const auto& fSet = refCast<const faceSet>(set);
-        subtractSet(fSet.name(), fSet.sortedToc(), boolList::null());
+        subtractSet
+        (
+            set.name(),
+            refCast<const faceSet>(set).sortedToc(),
+            boolList::null()
+        );
     }
 }
 
 
-void Foam::faceZoneSet::subtractSet(const labelUList& set)
+void Foam::faceZoneSet::subtractSet(const labelUList& elems)
 {
-    subtractSet(word::null, set, boolList::null());
+    subtractSet(word::null, elems, boolList::null());
 }
 
 
@@ -517,58 +538,51 @@ bool Foam::faceZoneSet::writeObject
 ) const
 {
     // Write shadow faceSet
-    word oldTypeName = typeName;
+    const word oldTypeName = typeName;
     const_cast<word&>(type()) = faceSet::typeName;
     bool ok = faceSet::writeObject(streamOpt, writeOnProc);
     const_cast<word&>(type()) = oldTypeName;
 
     // Modify faceZone
-    faceZoneMesh& faceZones = const_cast<polyMesh&>(mesh_).faceZones();
-    label zoneID = faceZones.findZoneID(name());
+    auto& zones = const_cast<polyMesh&>(mesh_).faceZones();
+    auto* zonePtr = zones.findZone(name());
 
-    if (zoneID == -1)
+    if (zonePtr)
     {
-        zoneID = faceZones.size();
-
-        faceZones.emplace_back
+        zonePtr->resetAddressing(addressing_, flipMap_);
+    }
+    else
+    {
+        zones.emplace_back
         (
             name(),
             addressing_,
             flipMap_,
-            zoneID,
-            faceZones
+            zones.size(),  // zoneID
+            zones
         );
     }
-    else
-    {
-        faceZones[zoneID].resetAddressing(addressing_, flipMap_);
-    }
-    faceZones.clearAddressing();
+    zones.clearAddressing();
 
-    return ok && faceZones.write(writeOnProc);
+    return ok && zones.write(writeOnProc);
 }
 
 
 void Foam::faceZoneSet::updateMesh(const mapPolyMesh& morphMap)
 {
-    // faceZone
-    labelList newAddressing(addressing_.size());
-    boolList newFlipMap(flipMap_.size(), false);
+    DynamicList<label> newAddressing(addressing_.size());
+    DynamicList<bool> newFlipMap(flipMap_.size());
 
-    label n = 0;
     forAll(addressing_, i)
     {
         label facei = addressing_[i];
         label newFacei = morphMap.reverseFaceMap()[facei];
         if (newFacei >= 0)
         {
-            newAddressing[n] = newFacei;
-            newFlipMap[n] = flipMap_[i];
-            n++;
+            newAddressing.push_back(newFacei);
+            newFlipMap.push_back(flipMap_[i]);
         }
     }
-    newAddressing.setSize(n);
-    newFlipMap.setSize(n);
 
     addressing_.transfer(newAddressing);
     flipMap_.transfer(newFlipMap);
diff --git a/src/meshTools/topoSet/topoSets/faceZoneSet.H b/src/meshTools/topoSet/topoSets/faceZoneSet.H
index 1f81d5d5d4..75adbdd7ae 100644
--- a/src/meshTools/topoSet/topoSets/faceZoneSet.H
+++ b/src/meshTools/topoSet/topoSets/faceZoneSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2022 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -89,7 +89,7 @@ class faceZoneSet
 public:
 
     //- Runtime type information
-    TypeName("faceZoneSet");
+    TypeNameNoDebug("faceZoneSet");
 
 
     // Constructors
@@ -103,16 +103,16 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct with initial size for labelHashSet
+        //- Construct empty (no-read) with initial labelHashSet capacity.
         faceZoneSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Copy construct from existing set
+        //- Copy construct (no-read) from existing set
         faceZoneSet
         (
             const polyMesh& mesh,
@@ -157,27 +157,24 @@ public:
         //  Insert all members [0,maxLen) which were not in set.
         virtual void invert(const label maxLen);
 
+        //- Subset contents. Only elements present in both sets remain.
+        virtual void subset(const labelUList& elems);
+
         //- Subset contents. Only elements present in both sets remain.
         virtual void subset(const topoSet& set);
 
-        //- Add elements present in set.
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Subtract elements present in set.
+        //- Subtract given elements from the set
+        virtual void subtractSet(const labelUList& elems);
+
+        //- Subtract given elements from the set
         virtual void subtractSet(const topoSet& set);
 
-        // Variants taking labelUList&
-
-            //- Subset contents. Only elements present in both sets remain.
-            virtual void subset(const labelUList& set);
-
-            //- Add elements present in set.
-            virtual void addSet(const labelUList& set);
-
-            //- Subtract elements present in set.
-            virtual void subtractSet(const labelUList& set);
-
-
         //- Sync faceZoneSet across coupled patches.
         virtual void sync(const polyMesh& mesh);
 
diff --git a/src/meshTools/topoSet/topoSets/pointBitSet.C b/src/meshTools/topoSet/topoSets/pointBitSet.C
index c0cc73297e..024fb5a08f 100644
--- a/src/meshTools/topoSet/topoSets/pointBitSet.C
+++ b/src/meshTools/topoSet/topoSets/pointBitSet.C
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -35,18 +35,12 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(pointBitSet, 0);
+    defineTypeName(pointBitSet);
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::pointBitSet::pointBitSet(const polyMesh& mesh)
-:
-    pointBitSet(mesh, false)
-{}
-
-
 Foam::pointBitSet::pointBitSet(const polyMesh& mesh, const bool val)
 :
     topoBitSet(mesh, "pointBitSet", mesh.nPoints(), val)
diff --git a/src/meshTools/topoSet/topoSets/pointBitSet.H b/src/meshTools/topoSet/topoSets/pointBitSet.H
index 557df281a5..7093fb6c37 100644
--- a/src/meshTools/topoSet/topoSets/pointBitSet.H
+++ b/src/meshTools/topoSet/topoSets/pointBitSet.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -56,16 +56,14 @@ class pointBitSet
 public:
 
     //- Runtime type information
-    TypeName("pointBitSet");
+    TypeNameNoDebug("pointBitSet");
 
 
     // Constructors
 
-        //- Construct with nPoints elements, all elements unset
-        explicit pointBitSet(const polyMesh& mesh);
-
-        //- Construct with nPoints elements, using initial val
-        pointBitSet(const polyMesh& mesh, const bool val);
+        //- Construct with nPoints elements,
+        //- all elements unset or initial value
+        explicit pointBitSet(const polyMesh& mesh, const bool val);
 
         //- Copy construct from bitset, resizing to nPoints elements as required
         pointBitSet(const polyMesh& mesh, const bitSet& bits);
diff --git a/src/meshTools/topoSet/topoSets/pointSet.C b/src/meshTools/topoSet/topoSets/pointSet.C
index 6c4bc3a862..92931c3de3 100644
--- a/src/meshTools/topoSet/topoSets/pointSet.C
+++ b/src/meshTools/topoSet/topoSets/pointSet.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,13 +37,14 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(pointSet, 0);
+    defineTypeName(pointSet);
     addToRunTimeSelectionTable(topoSet, pointSet, word);
     addToRunTimeSelectionTable(topoSet, pointSet, size);
     addToRunTimeSelectionTable(topoSet, pointSet, set);
 }
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::pointSet::pointSet(const IOobject& io)
 :
@@ -51,17 +52,24 @@ Foam::pointSet::pointSet(const IOobject& io)
 {}
 
 
+Foam::pointSet::pointSet(const IOobject& io, const Foam::zero)
+:
+    topoSet(io, Foam::zero{})
+{}
+
+
 Foam::pointSet::pointSet
 (
     const polyMesh& mesh,
     const word& name,
     IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
 )
 :
-    topoSet(mesh, typeName, name, rOpt, wOpt)
+    topoSet(mesh, typeName, name, rOpt, wOpt, reg)
 {
-    check(mesh.nPoints());
+    check(mesh.nPoints());  // Valid range?
 }
 
 
@@ -69,11 +77,11 @@ Foam::pointSet::pointSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    const  label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    topoSet(mesh, name, size, wOpt)
+    topoSet(mesh, name, initialCapacity, wOpt)
 {}
 
 
@@ -125,6 +133,28 @@ Foam::pointSet::pointSet
 {}
 
 
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+Foam::labelHashSet Foam::pointSet::readContents
+(
+    const polyMesh& mesh,
+    const word& name
+)
+{
+    pointSet reader
+    (
+        topoSet::findIOobject(mesh, name, IOobjectOption::NO_REGISTER),
+        Foam::zero{}
+    );
+
+    labelHashSet labels;
+    reader.readIOcontents(typeName, labels);
+    reader.checkLabels(labels, mesh.nPoints());  // Valid range?
+
+    return labels;
+}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 void Foam::pointSet::sync(const polyMesh& mesh)
diff --git a/src/meshTools/topoSet/topoSets/pointSet.H b/src/meshTools/topoSet/topoSets/pointSet.H
index eff97e122c..46da2cef6a 100644
--- a/src/meshTools/topoSet/topoSets/pointSet.H
+++ b/src/meshTools/topoSet/topoSets/pointSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2016-2022 OpenCFD Ltd.
+    Copyright (C) 2016-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -56,7 +56,7 @@ class pointSet
 public:
 
     //- Runtime type information
-    TypeName("pointSet");
+    TypeNameNoDebug("pointSet");
 
 
     // Constructors
@@ -64,25 +64,42 @@ public:
         //- Construct from IOobject
         explicit pointSet(const IOobject& io);
 
-        //- Construct from objectRegistry and name
+        //- Construct empty (no-read) with IOobject information
+        pointSet(const IOobject& io, const Foam::zero);
+
+        //- Construct from polyMesh (registry) and name
         pointSet
         (
             const polyMesh& mesh,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct empty with initial size for labelHashSet
+        //- Construct from polyMesh (registry), name and registration option
         pointSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            IOobjectOption::registerOption reg,
+            IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        )
+        :
+            pointSet(mesh, name, rOpt, wOpt, reg)
+        {}
+
+        //- Construct empty (no-read) with initial labelHashSet capacity.
+        pointSet
+        (
+            const polyMesh& mesh,
+            const word& name,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct from existing set
+        //- Copy construct (no-read) from existing set
         pointSet
         (
             const polyMesh& mesh,
@@ -91,7 +108,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy of labelHashSet
+        //- Copy construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         pointSet
         (
             const polyMesh& mesh,
@@ -100,7 +118,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with moving labelHashSet
+        //- Move construct (no-read) from labelHashSet,
+        //- with search for IOobject instance.
         pointSet
         (
             const polyMesh& mesh,
@@ -109,7 +128,8 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct (no-read) with copy of labels
+        //- Copy construct (no-read) from labels,
+        //- with search for IOobject instance.
         pointSet
         (
             const polyMesh& mesh,
@@ -119,11 +139,21 @@ public:
         );
 
 
+    // Factory Methods
+
+        //- Read and return contents. Intermediate IOobject is not registered
+        static labelHashSet readContents
+        (
+            const polyMesh& mesh,
+            const word& name
+        );
+
+
     //- Destructor
     virtual ~pointSet() = default;
 
 
-    // Member functions
+    // Member Functions
 
         //- Sync set across coupled patches. Adds coupled points to set.
         virtual void sync(const polyMesh& mesh);
diff --git a/src/meshTools/topoSet/topoSets/pointZoneSet.C b/src/meshTools/topoSet/topoSets/pointZoneSet.C
index 1bcd5b503d..59b612d0f5 100644
--- a/src/meshTools/topoSet/topoSets/pointZoneSet.C
+++ b/src/meshTools/topoSet/topoSets/pointZoneSet.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2022,2024 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,18 +37,18 @@ License
 
 namespace Foam
 {
-    defineTypeNameAndDebug(pointZoneSet, 0);
+    defineTypeName(pointZoneSet);
     addToRunTimeSelectionTable(topoSet, pointZoneSet, word);
     addToRunTimeSelectionTable(topoSet, pointZoneSet, size);
     addToRunTimeSelectionTable(topoSet, pointZoneSet, set);
 }
 
+
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
 void Foam::pointZoneSet::updateSet()
 {
-    labelList order(sortedOrder(addressing_));
-    inplaceReorder(order, addressing_);
+    Foam::sort(addressing_);
 
     pointSet::clearStorage();
     pointSet::reserve(addressing_.size());
@@ -62,46 +62,46 @@ Foam::pointZoneSet::pointZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    IOobjectOption::readOption rOpt,
+    const label initialCapacity,
     IOobjectOption::writeOption wOpt
 )
 :
-    pointSet(mesh, name, 1024),  // do not read pointSet
-    mesh_(mesh),
-    addressing_()
-{
-    const pointZoneMesh& pointZones = mesh.pointZones();
-    label zoneID = pointZones.findZoneID(name);
-
-    if
-    (
-         IOobjectOption::isReadRequired(rOpt)
-     || (IOobjectOption::isReadOptional(rOpt) && zoneID != -1)
-    )
-    {
-        const pointZone& fz = pointZones[zoneID];
-        addressing_ = fz;
-    }
-
-    updateSet();
-
-    check(mesh.nPoints());
-}
+    pointSet(mesh, name, initialCapacity, wOpt),  // Construct no-read
+    mesh_(mesh)
+{}
 
 
 Foam::pointZoneSet::pointZoneSet
 (
     const polyMesh& mesh,
     const word& name,
-    const label size,
+    IOobjectOption::readOption rOpt,
     IOobjectOption::writeOption wOpt
 )
 :
-    pointSet(mesh, name, size, wOpt),
-    mesh_(mesh),
-    addressing_()
+    pointZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto& zones = mesh.pointZones();
+    const auto* zonePtr = zones.cfindZone(name);
+
+    if (!zonePtr)
+    {
+        if (IOobjectOption::isReadRequired(rOpt))
+        {
+            FatalErrorInFunction
+                << "Zone named " << name << " not found.  "
+                << "List of available zone names: " << zones.names() << nl
+                << exit(FatalError);
+        }
+    }
+    else if (IOobjectOption::isAnyRead(rOpt))
+    {
+        const auto& zn = *zonePtr;
+        addressing_ = zn;
+    }
+
     updateSet();
+    check(mesh.nPoints());
 }
 
 
@@ -113,15 +113,19 @@ Foam::pointZoneSet::pointZoneSet
     IOobjectOption::writeOption wOpt
 )
 :
-    pointSet(mesh, name, set.size(), wOpt),
-    mesh_(mesh),
-    addressing_
-    (
-        isA<const pointZoneSet>(set)
-      ? refCast<const pointZoneSet>(set).addressing()
-      : set.sortedToc()
-    )
+    pointZoneSet(mesh, name, label(0), wOpt)  // Construct no-read
 {
+    const auto* zonePtr = isA<pointZoneSet>(set);
+
+    if (zonePtr)
+    {
+        addressing_ = zonePtr->addressing();
+    }
+    else
+    {
+        addressing_ = set.sortedToc();
+    }
+
     updateSet();
 }
 
@@ -133,23 +137,23 @@ void Foam::pointZoneSet::invert(const label maxLen)
     // Count
     label n = 0;
 
-    for (label pointi = 0; pointi < maxLen; ++pointi)
+    for (label id = 0; id < maxLen; ++id)
     {
-        if (!found(pointi))
+        if (!found(id))
         {
             ++n;
         }
     }
 
     // Fill
-    addressing_.setSize(n);
+    addressing_.resize_nocopy(n);
     n = 0;
 
-    for (label pointi = 0; pointi < maxLen; ++pointi)
+    for (label id = 0; id < maxLen; ++id)
     {
-        if (!found(pointi))
+        if (!found(id))
         {
-            addressing_[n] = pointi;
+            addressing_[n] = id;
             ++n;
         }
     }
@@ -157,31 +161,15 @@ void Foam::pointZoneSet::invert(const label maxLen)
 }
 
 
-void Foam::pointZoneSet::subset(const topoSet& set)
+void Foam::pointZoneSet::subset(const labelUList& elems)
 {
     DynamicList<label> newAddressing(addressing_.size());
 
-    const auto* setPtr = dynamic_cast<const pointZoneSet*>(&set);
-
-    if (setPtr)
+    for (const label id : elems)
     {
-        for (const label pointi : setPtr->addressing())
+        if (found(id))
         {
-            if (found(pointi))
-            {
-                newAddressing.append(pointi);
-            }
-        }
-    }
-    else
-    {
-        // Assume a pointSet
-        for (const label pointi : refCast<const pointSet>(set).sortedToc())
-        {
-            if (found(pointi))
-            {
-                newAddressing.append(pointi);
-            }
+            newAddressing.push_back(id);
         }
     }
 
@@ -190,15 +178,32 @@ void Foam::pointZoneSet::subset(const topoSet& set)
 }
 
 
-void Foam::pointZoneSet::subset(const labelUList& set)
+void Foam::pointZoneSet::subset(const topoSet& set)
 {
-    DynamicList<label> newAddressing(addressing_.size());
+    const auto* zonePtr = isA<pointZoneSet>(set);
 
-    for (const label pointi : set)
+    if (zonePtr)
     {
-        if (found(pointi))
+        // Is a pointZoneSet
+        this->subset(zonePtr->addressing());
+    }
+    else
+    {
+        // Assume a pointSet
+        this->subset(refCast<const pointSet>(set).sortedToc());
+    }
+}
+
+
+void Foam::pointZoneSet::addSet(const labelUList& elems)
+{
+    DynamicList<label> newAddressing(addressing_);
+
+    for (const label id : elems)
+    {
+        if (!found(id))
         {
-            newAddressing.append(pointi);
+            newAddressing.push_back(id);
         }
     }
 
@@ -209,46 +214,33 @@ void Foam::pointZoneSet::subset(const labelUList& set)
 
 void Foam::pointZoneSet::addSet(const topoSet& set)
 {
-    DynamicList<label> newAddressing(addressing_);
+    const auto* zonePtr = isA<pointZoneSet>(set);
 
-    const auto* setPtr = dynamic_cast<const pointZoneSet*>(&set);
-
-    if (setPtr)
+    if (zonePtr)
     {
-        for (const label pointi : setPtr->addressing())
-        {
-            if (!found(pointi))
-            {
-                newAddressing.append(pointi);
-            }
-        }
+        // Is a pointZoneSet
+        this->addSet(zonePtr->addressing());
     }
     else
     {
         // Assume a pointSet
-        for (const label pointi : refCast<const pointSet>(set).sortedToc())
-        {
-            if (!found(pointi))
-            {
-                newAddressing.append(pointi);
-            }
-        }
+        this->addSet(refCast<const pointSet>(set).sortedToc());
     }
-
-    addressing_.transfer(newAddressing);
-    updateSet();
 }
 
 
-void Foam::pointZoneSet::addSet(const labelUList& set)
+void Foam::pointZoneSet::subtractSet(const labelUList& elems)
 {
-    DynamicList<label> newAddressing(addressing_);
+    DynamicList<label> newAddressing(addressing_.size());
 
-    for (const label pointi : set)
+    const labelHashSet set(elems);
+
+    for (const label id : addressing_)
     {
-        if (!found(pointi))
+        if (!set.found(id))
         {
-            newAddressing.append(pointi);
+            // Retain if not in the topoSet (parameter)
+            newAddressing.push_back(id);
         }
     }
 
@@ -261,32 +253,12 @@ void Foam::pointZoneSet::subtractSet(const topoSet& set)
 {
     DynamicList<label> newAddressing(addressing_.size());
 
-    for (label pointi : addressing_)
+    for (const label id : addressing_)
     {
-        if (!set.found(pointi))
+        if (!set.found(id))
         {
-            // Not found in zoneSet so add
-            newAddressing.append(pointi);
-        }
-    }
-
-    addressing_.transfer(newAddressing);
-    updateSet();
-}
-
-
-void Foam::pointZoneSet::subtractSet(const labelUList& elems)
-{
-    DynamicList<label> newAddressing(addressing_.size());
-
-    const labelHashSet zoneSet(elems);
-
-    for (const label pointi : addressing_)
-    {
-        if (!zoneSet.found(pointi))
-        {
-            // Not found in zoneSet so add
-            newAddressing.append(pointi);
+            // Retain if not in the topoSet (parameter)
+            newAddressing.push_back(id);
         }
     }
 
@@ -318,56 +290,49 @@ bool Foam::pointZoneSet::writeObject
 ) const
 {
     // Write shadow pointSet
-    word oldTypeName = typeName;
+    const word oldTypeName = typeName;
     const_cast<word&>(type()) = pointSet::typeName;
     bool ok = pointSet::writeObject(streamOpt, writeOnProc);
     const_cast<word&>(type()) = oldTypeName;
 
     // Modify pointZone
-    pointZoneMesh& pointZones = const_cast<polyMesh&>(mesh_).pointZones();
-    label zoneID = pointZones.findZoneID(name());
+    auto& zones = const_cast<polyMesh&>(mesh_).pointZones();
+    auto* zonePtr = zones.findZone(name());
 
-    if (zoneID == -1)
+    if (zonePtr)
     {
-        zoneID = pointZones.size();
-
-        pointZones.emplace_back
-        (
-            name(),
-            addressing_,
-            zoneID,
-            pointZones
-        );
+        zonePtr->resetAddressing(addressing_);
     }
     else
     {
-        pointZones[zoneID] = addressing_;
+        zones.emplace_back
+        (
+            name(),
+            addressing_,
+            zones.size(),  // zoneID
+            zones
+        );
     }
-    pointZones.clearAddressing();
+    zones.clearAddressing();
 
-    return ok && pointZones.write(writeOnProc);
+    return ok && zones.write(writeOnProc);
 }
 
 
 void Foam::pointZoneSet::updateMesh(const mapPolyMesh& morphMap)
 {
-    // pointZone
-    labelList newAddressing(addressing_.size());
+    DynamicList<label> newAddressing(addressing_.size());
 
-    label n = 0;
     for (const label pointi : addressing_)
     {
         const label newPointi = morphMap.reversePointMap()[pointi];
         if (newPointi >= 0)
         {
-            newAddressing[n] = newPointi;
-            ++n;
+            newAddressing.push_back(newPointi);
         }
     }
-    newAddressing.resize(n);
 
     addressing_.transfer(newAddressing);
-
     updateSet();
 }
 
diff --git a/src/meshTools/topoSet/topoSets/pointZoneSet.H b/src/meshTools/topoSet/topoSets/pointZoneSet.H
index e1419f51cf..98aabecd1e 100644
--- a/src/meshTools/topoSet/topoSets/pointZoneSet.H
+++ b/src/meshTools/topoSet/topoSets/pointZoneSet.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2022 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -60,11 +60,10 @@ class pointZoneSet
 
         labelList addressing_;
 
-
 public:
 
     //- Runtime type information
-    TypeName("pointZoneSet");
+    TypeNameNoDebug("pointZoneSet");
 
 
     // Constructors
@@ -78,16 +77,16 @@ public:
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Construct empty with initial size for labelHashSet
+        //- Construct empty (no-read) with initial labelHashSet capacity.
         pointZoneSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
+            const label initialCapacity,
             IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
         );
 
-        //- Copy construct from existing set
+        //- Copy construct (no-read) from existing set
         pointZoneSet
         (
             const polyMesh& mesh,
@@ -101,18 +100,19 @@ public:
     virtual ~pointZoneSet() = default;
 
 
-    // Member functions
+    // Member Functions
 
-        const labelList& addressing() const
+        const labelList& addressing() const noexcept
         {
             return addressing_;
         }
 
-        labelList& addressing()
+        labelList& addressing() noexcept
         {
             return addressing_;
         }
 
+
         //- Sort addressing and make pointSet part consistent with addressing
         void updateSet();
 
@@ -120,26 +120,24 @@ public:
         //  Insert all members [0,maxLen) which were not in set
         virtual void invert(const label maxLen);
 
+        //- Subset contents. Only elements present in both sets remain.
+        virtual void subset(const labelUList& elems);
+
         //- Subset contents. Only elements present in both sets remain.
         virtual void subset(const topoSet& set);
 
-        //- Add elements present in set.
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Subtract elements present in set.
+        //- Subtract given elements from the set
+        virtual void subtractSet(const labelUList& elems);
+
+        //- Subtract given elements from the set
         virtual void subtractSet(const topoSet& set);
 
-        // Variants taking labelUList&
-
-            //- Subset contents. Only elements present in both sets remain.
-            virtual void subset(const labelUList& set);
-
-            //- Add elements present in set.
-            virtual void addSet(const labelUList& set);
-
-            //- Subtract elements present in set.
-            virtual void subtractSet(const labelUList& set);
-
 
         //- Sync pointZoneSet across coupled patches.
         virtual void sync(const polyMesh& mesh);
diff --git a/src/meshTools/topoSet/topoSets/topoBitSet.C b/src/meshTools/topoSet/topoSets/topoBitSet.C
index 6bd7005d5e..f6d44ca25d 100644
--- a/src/meshTools/topoSet/topoSets/topoBitSet.C
+++ b/src/meshTools/topoSet/topoSets/topoBitSet.C
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2024 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -126,9 +126,8 @@ Foam::topoBitSet::topoBitSet
             IOobject::NO_WRITE,
             IOobject::NO_REGISTER
         ),
-        label(0)  // zero-sized (unallocated) labelHashSet
-    ),
-    selected_()
+        Foam::zero{}  // Empty labelHashSet (initialCapacity = 0)
+    )
 {}
 
 
@@ -178,6 +177,12 @@ Foam::topoBitSet::topoBitSet
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+bool Foam::topoBitSet::contains(const label id) const
+{
+    return selected_.test(id);
+}
+
+
 bool Foam::topoBitSet::found(const label id) const
 {
     return selected_.test(id);
@@ -218,9 +223,12 @@ void Foam::topoBitSet::invert(const label maxLen)
 void Foam::topoBitSet::subset(const topoSet& set)
 {
     // Only retain entries found in both sets
-    if (isA<topoBitSet>(set))
+
+    const auto* topoBitsPtr = isA<topoBitSet>(set);
+
+    if (topoBitsPtr)
     {
-        selected_ &= refCast<const topoBitSet>(set).selected_;
+        selected_ &= topoBitsPtr->selected_;
     }
     else if (set.empty())
     {
@@ -242,25 +250,27 @@ void Foam::topoBitSet::subset(const topoSet& set)
 void Foam::topoBitSet::subset(const labelUList& elems)
 {
     // Only retain entries found in both sets
-    bitSet newSelected(selected_.size());
+    bitSet newLabels(selected_.size());
 
     for (const label id : elems)
     {
-        if (selected_[id])
+        if (selected_.test(id))
         {
-            newSelected.set(id);
+            newLabels.set(id);
         }
     }
-    selected_ = newSelected;
+    selected_.transfer(newLabels);
 }
 
 
 void Foam::topoBitSet::addSet(const topoSet& set)
 {
     // Add entries to the set
-    if (isA<topoBitSet>(set))
+    const auto* topoBitsPtr = isA<topoBitSet>(set);
+
+    if (topoBitsPtr)
     {
-        selected_ |= refCast<const topoBitSet>(set).selected_;
+        selected_ |= topoBitsPtr->selected_;
     }
     else
     {
@@ -281,9 +291,11 @@ void Foam::topoBitSet::addSet(const labelUList& elems)
 void Foam::topoBitSet::subtractSet(const topoSet& set)
 {
     // Subtract entries from the set
-    if (isA<topoBitSet>(set))
+    const auto* topoBitsPtr = isA<topoBitSet>(set);
+
+    if (topoBitsPtr)
     {
-        selected_ -= refCast<const topoBitSet>(set).selected_;
+        selected_ -= topoBitsPtr->selected_;
     }
     else
     {
diff --git a/src/meshTools/topoSet/topoSets/topoBitSet.H b/src/meshTools/topoSet/topoSets/topoBitSet.H
index ae702fb71f..5123a1dcb4 100644
--- a/src/meshTools/topoSet/topoSets/topoBitSet.H
+++ b/src/meshTools/topoSet/topoSets/topoBitSet.H
@@ -70,10 +70,10 @@ protected:
         virtual void check(const label maxSize);
 
 
-        //- Construct with empty selection
+        //- Construct (no-read) with empty selection
         topoBitSet(const polyMesh& mesh, const word& setName);
 
-        //- Construct with size elements
+        //- Construct (no-read) with \c size elements of initial value
         topoBitSet
         (
             const polyMesh& mesh,
@@ -82,7 +82,7 @@ protected:
             const bool val
         );
 
-        //- Copy construct with bitset values, size elements
+        //- Copy construct from bitset values, size elements
         topoBitSet
         (
             const polyMesh& mesh,
@@ -91,7 +91,7 @@ protected:
             const bitSet& bits
         );
 
-        //- Move construct with bitset values, size elements
+        //- Move construct from bitset values, size elements
         topoBitSet
         (
             const polyMesh& mesh,
@@ -127,6 +127,9 @@ public:
             selected_.reset();
         }
 
+        //- Has the given index?
+        virtual bool contains(const label id) const;
+
         //- Has the given index?
         virtual bool found(const label id) const;
 
@@ -146,25 +149,23 @@ public:
         //  Insert all members [0,maxLen) which were not in set.
         virtual void invert(const label maxLen);
 
+        //- Subset contents. Only elements present in both sets remain.
+        virtual void subset(const labelUList& elems);
+
         //- Subset contents. Only elements present in both sets remain.
         virtual void subset(const topoSet& set);
 
-        //- Add elements present in set.
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Subtract elements present in set.
+        //- Subtract given elements from the set
+        virtual void subtractSet(const labelUList& elems);
+
+        //- Subtract given elements from the set
         virtual void subtractSet(const topoSet& set);
-
-        // Variants taking labelUList&
-
-            //- Subset contents. Only elements present in both sets remain.
-            virtual void subset(const labelUList& set);
-
-            //- Add elements present in set.
-            virtual void addSet(const labelUList& set);
-
-            //- Subtract elements present in set.
-            virtual void subtractSet(const labelUList& set);
 };
 
 
diff --git a/src/meshTools/topoSet/topoSets/topoBoolSet.C b/src/meshTools/topoSet/topoSets/topoBoolSet.C
index 0045c159f3..4f2ae71a9d 100644
--- a/src/meshTools/topoSet/topoSets/topoBoolSet.C
+++ b/src/meshTools/topoSet/topoSets/topoBoolSet.C
@@ -135,9 +135,8 @@ Foam::topoBoolSet::topoBoolSet
             IOobject::NO_WRITE,
             IOobject::NO_REGISTER
         ),
-        label(0)  // zero-sized (unallocated) labelHashSet
-    ),
-    selected_()
+        Foam::zero{}  // Empty labelHashSet (initialCapacity = 0)
+    )
 {}
 
 
@@ -187,6 +186,12 @@ Foam::topoBoolSet::topoBoolSet
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+bool Foam::topoBoolSet::contains(const label id) const
+{
+    return selected_.test(id);
+}
+
+
 bool Foam::topoBoolSet::found(const label id) const
 {
     return selected_.test(id);
diff --git a/src/meshTools/topoSet/topoSets/topoBoolSet.H b/src/meshTools/topoSet/topoSets/topoBoolSet.H
index 273e3297f9..a28557d3be 100644
--- a/src/meshTools/topoSet/topoSets/topoBoolSet.H
+++ b/src/meshTools/topoSet/topoSets/topoBoolSet.H
@@ -70,10 +70,10 @@ protected:
         virtual void check(const label maxSize);
 
 
-        //- Construct with empty selection
+        //- Construct (no-read) with empty selection
         topoBoolSet(const polyMesh& mesh, const word& setName);
 
-        //- Construct with size elements
+        //- Construct (no-read) with \c size elements of initial value
         topoBoolSet
         (
             const polyMesh& mesh,
@@ -100,7 +100,6 @@ protected:
             boolList&& bools
         );
 
-
 public:
 
     //- Destructor
@@ -127,6 +126,9 @@ public:
             selected_ = false;
         }
 
+        //- Has the given index?
+        virtual bool contains(const label id) const;
+
         //- Has the given index?
         virtual bool found(const label id) const;
 
@@ -146,25 +148,23 @@ public:
         //  Insert all members [0,maxLen) which were not in set.
         virtual void invert(const label maxLen);
 
+        //- Subset contents. Only elements present in both sets remain.
+        virtual void subset(const labelUList& elems);
+
         //- Subset contents. Only elements present in both sets remain.
         virtual void subset(const topoSet& set);
 
-        //- Add elements present in set.
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Subtract elements present in set.
+        //- Subtract given elements from the set.
+        virtual void subtractSet(const labelUList& elems);
+
+        //- Subtract given elements from the set.
         virtual void subtractSet(const topoSet& set);
-
-        // Variants taking labelUList&
-
-            //- Subset contents. Only elements present in both sets remain.
-            virtual void subset(const labelUList& set);
-
-            //- Add elements present in set.
-            virtual void addSet(const labelUList& set);
-
-            //- Subtract elements present in set.
-            virtual void subtractSet(const labelUList& set);
 };
 
 
diff --git a/src/meshTools/topoSet/topoSets/topoSet.C b/src/meshTools/topoSet/topoSets/topoSet.C
index 29d2a8cb1c..0d8c64cbbe 100644
--- a/src/meshTools/topoSet/topoSets/topoSet.C
+++ b/src/meshTools/topoSet/topoSets/topoSet.C
@@ -140,6 +140,30 @@ Foam::fileName Foam::topoSet::localPath
 }
 
 
+// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
+
+bool Foam::topoSet::readIOcontents
+(
+    const word& wantedType,
+    labelHashSet& contents
+)
+{
+    if (isReadRequired() || (isReadOptional() && headerOk()))
+    {
+        Istream& is = readStream(wantedType);
+
+        if (is.good())
+        {
+            is >> contents;
+            close();
+        }
+        return true;
+    }
+
+    return false;
+}
+
+
 // * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //
 
 // Update stored cell numbers using map.
@@ -200,10 +224,8 @@ void Foam::topoSet::updateLabels(const labelUList& map)
 }
 
 
-void Foam::topoSet::check(const label maxSize)
+void Foam::topoSet::checkLabels(const labelUList& labels, const label maxSize)
 {
-    const labelHashSet& labels = *this;
-
     for (const label oldId : labels)
     {
         if (oldId < 0 || oldId >= maxSize)
@@ -211,21 +233,41 @@ void Foam::topoSet::check(const label maxSize)
             FatalErrorInFunction
                 << "Illegal content " << oldId << " of set:" << name()
                 << " of type " << type() << nl
-                << "Value should be between [0," << maxSize << ')'
-                << endl
+                << "Value should be between [0," << maxSize << ')' << nl
                 << abort(FatalError);
         }
     }
 }
 
 
-// Write maxElem elements, starting at iter. Updates iter and elemI.
-void Foam::topoSet::writeDebug
+void Foam::topoSet::checkLabels(const labelHashSet& labels, const label maxSize)
+{
+    for (const label oldId : labels)
+    {
+        if (oldId < 0 || oldId >= maxSize)
+        {
+            FatalErrorInFunction
+                << "Illegal content " << oldId << " of set:" << name()
+                << " of type " << type() << nl
+                << "Value should be between [0," << maxSize << ')' << nl
+                << abort(FatalError);
+        }
+    }
+}
+
+
+void Foam::topoSet::check(const label maxSize)
+{
+    checkLabels(*this, maxSize);
+}
+
+
+// Write maxElem elements, starting at iter. Updates iter
+Foam::label Foam::topoSet::writeDebug
 (
     Ostream& os,
     const label maxElem,
-    topoSet::const_iterator& iter,
-    label& elemI
+    labelHashSet::const_iterator& iter
 ) const
 {
     label n = 0;
@@ -239,19 +281,19 @@ void Foam::topoSet::writeDebug
         os << iter.key() << ' ';
 
         ++n;
-        ++elemI;
     }
+
+    return n;
 }
 
 
-// Write maxElem elements, starting at iter. Updates iter and elemI.
-void Foam::topoSet::writeDebug
+// Write maxElem elements, starting at iter. Updates iter
+Foam::label Foam::topoSet::writeDebug
 (
     Ostream& os,
     const pointField& coords,
     const label maxElem,
-    topoSet::const_iterator& iter,
-    label& elemI
+    labelHashSet::const_iterator& iter
 ) const
 {
     label n = 0;
@@ -265,8 +307,9 @@ void Foam::topoSet::writeDebug
         os << iter.key() << coords[iter.key()] << ' ';
 
         ++n;
-        ++elemI;
     }
+
+    return n;
 }
 
 
@@ -283,22 +326,20 @@ void Foam::topoSet::writeDebug
     os  << "Set bounding box: min = "
         << bb.min() << "    max = " << bb.max() << " metres." << nl << endl;
 
-    label n = 0;
-
-    topoSet::const_iterator iter = this->cbegin();
+    labelHashSet::const_iterator iter = labelHashSet::cbegin();
 
     if (size() <= maxLen)
     {
-        writeDebug(os, coords, maxLen, iter, n);
+        writeDebug(os, coords, maxLen, iter);
     }
     else
     {
-        label halfLen = maxLen/2;
+        const label halfLen = maxLen/2;
 
         os  << "Size larger than " << maxLen << ". Printing first and last "
             << halfLen << " elements:" << nl << endl;
 
-        writeDebug(os, coords, halfLen, iter, n);
+        label n = writeDebug(os, coords, halfLen, iter);
 
         os  << nl << "  .." << nl << endl;
 
@@ -307,7 +348,7 @@ void Foam::topoSet::writeDebug
             ++iter;
         }
 
-        writeDebug(os, coords, halfLen, iter, n);
+        writeDebug(os, coords, halfLen, iter);
     }
 }
 
@@ -319,7 +360,8 @@ Foam::IOobject Foam::topoSet::findIOobject
     const polyMesh& mesh,
     const word& name,
     IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
 )
 {
     IOobject io
@@ -329,13 +371,14 @@ Foam::IOobject Foam::topoSet::findIOobject
         (
             mesh.meshDir()/"sets",
             word::null,
-            IOobject::READ_IF_PRESENT,
+            IOobjectOption::READ_IF_PRESENT,
             mesh.facesInstance()
         ),
         polyMesh::meshSubDir/"sets",
         mesh,
         rOpt,
-        wOpt
+        wOpt,
+        reg
     );
 
     if (!io.typeHeaderOk<topoSet>(false) && disallowGenericSets != 0)
@@ -353,7 +396,8 @@ Foam::IOobject Foam::topoSet::findIOobject
     const Time& runTime,
     const word& name,
     IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
 )
 {
     return IOobject
@@ -364,6 +408,8 @@ Foam::IOobject Foam::topoSet::findIOobject
             polyMesh::meshSubDir/"sets",
             word::null,
             IOobject::MUST_READ,
+
+            // The stop instance with "polyMesh/faces"
             runTime.findInstance
             (
                 polyMesh::meshSubDir,
@@ -374,7 +420,8 @@ Foam::IOobject Foam::topoSet::findIOobject
         polyMesh::meshSubDir/"sets",
         runTime,
         rOpt,
-        wOpt
+        wOpt,
+        reg
     );
 }
 
@@ -385,97 +432,20 @@ Foam::topoSet::topoSet(const IOobject& io, const word& wantedType)
 :
     regIOobject(io)
 {
-    if (isReadRequired() || (isReadOptional() && headerOk()))
-    {
-        if (readStream(wantedType).good())
-        {
-            readStream(wantedType) >> static_cast<labelHashSet&>(*this);
-
-            close();
-        }
-    }
+    readIOcontents(wantedType, static_cast<labelHashSet&>(*this));
 }
 
 
-Foam::topoSet::topoSet
-(
-    const polyMesh& mesh,
-    const word& wantedType,
-    const word& name,
-    IOobjectOption::readOption rOpt,
-    IOobjectOption::writeOption wOpt
-)
+Foam::topoSet::topoSet(const IOobject& io, const Foam::zero)
 :
-    regIOobject(findIOobject(mesh, name, rOpt, wOpt))
-{
-    if (isReadRequired() || (isReadOptional() && headerOk()))
-    {
-        if (readStream(wantedType).good())
-        {
-            readStream(wantedType) >> static_cast<labelHashSet&>(*this);
-
-            close();
-        }
-    }
-}
-
-
-Foam::topoSet::topoSet
-(
-    const polyMesh& mesh,
-    const word& name,
-    const label size,
-    IOobjectOption::writeOption wOpt
-)
-:
-    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt)),
-    labelHashSet(size)
+    regIOobject(io)
 {}
 
 
-Foam::topoSet::topoSet
-(
-    const polyMesh& mesh,
-    const word& name,
-    const labelHashSet& labels,
-    IOobjectOption::writeOption wOpt
-)
-:
-    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt)),
-    labelHashSet(labels)
-{}
-
-
-Foam::topoSet::topoSet
-(
-    const polyMesh& mesh,
-    const word& name,
-    labelHashSet&& labels,
-    IOobjectOption::writeOption wOpt
-)
-:
-    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt)),
-    labelHashSet(std::move(labels))
-{}
-
-
-Foam::topoSet::topoSet
-(
-    const polyMesh& mesh,
-    const word& name,
-    const labelUList& labels,
-    IOobjectOption::writeOption wOpt
-)
-:
-    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt)),
-    labelHashSet(labels)
-{}
-
-
-Foam::topoSet::topoSet(const IOobject& io, const label size)
+Foam::topoSet::topoSet(const IOobject& io, const label initialCapacity)
 :
     regIOobject(io),
-    labelHashSet(size)
+    labelHashSet(initialCapacity)
 {}
 
 
@@ -493,11 +463,89 @@ Foam::topoSet::topoSet(const IOobject& io, labelHashSet&& labels)
 {}
 
 
+Foam::topoSet::topoSet
+(
+    const polyMesh& mesh,
+    const word& wantedType,
+    const word& name,
+    IOobjectOption::readOption rOpt,
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
+)
+:
+    regIOobject(findIOobject(mesh, name, rOpt, wOpt, reg))
+{
+    readIOcontents(wantedType, static_cast<labelHashSet&>(*this));
+}
+
+
+Foam::topoSet::topoSet
+(
+    const polyMesh& mesh,
+    const word& name,
+    const label initialCapacity,
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
+)
+:
+    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt, reg)),
+    labelHashSet(initialCapacity)
+{}
+
+
+Foam::topoSet::topoSet
+(
+    const polyMesh& mesh,
+    const word& name,
+    const labelHashSet& labels,
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
+)
+:
+    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt, reg)),
+    labelHashSet(labels)
+{}
+
+
+Foam::topoSet::topoSet
+(
+    const polyMesh& mesh,
+    const word& name,
+    labelHashSet&& labels,
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
+)
+:
+    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt, reg)),
+    labelHashSet(std::move(labels))
+{}
+
+
+Foam::topoSet::topoSet
+(
+    const polyMesh& mesh,
+    const word& name,
+    const labelUList& labels,
+    IOobjectOption::writeOption wOpt,
+    IOobjectOption::registerOption reg
+)
+:
+    regIOobject(findIOobject(mesh, name, IOobject::NO_READ, wOpt, reg)),
+    labelHashSet(labels)
+{}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+bool Foam::topoSet::contains(const label id) const
+{
+    return static_cast<const labelHashSet&>(*this).contains(id);
+}
+
+
 bool Foam::topoSet::found(const label id) const
 {
-    return static_cast<const labelHashSet&>(*this).found(id);
+    return static_cast<const labelHashSet&>(*this).contains(id);
 }
 
 
@@ -534,13 +582,13 @@ void Foam::topoSet::invert(const label maxLen)
     );
 
     clear();  // Maybe don't trust the previous move operation
-    reserve(max(64, (maxLen - original.size())));
+    reserve(Foam::max(64, (maxLen - original.size())));
 
-    for (label id=0; id < maxLen; ++id)
+    for (label id = 0; id < maxLen; ++id)
     {
-        if (!original.found(id))
+        if (!original.contains(id))
         {
-            this->set(id);
+            labelHashSet::set(id);
         }
     }
 }
@@ -558,10 +606,11 @@ void Foam::topoSet::subset(const labelUList& elems)
     // Only retain entries found in both sets
     auto& currentSet = static_cast<labelHashSet&>(*this);
 
-    DynamicList<label> newElems(elems.size()+currentSet.size());
+    DynamicList<label> newElems(Foam::min(elems.size(), currentSet.size()));
+
     for (const label elem : elems)
     {
-        if (currentSet.found(elem))
+        if (currentSet.contains(elem))
         {
             newElems.push_back(elem);
         }
@@ -609,22 +658,20 @@ void Foam::topoSet::sync(const polyMesh&)
 
 void Foam::topoSet::writeDebug(Ostream& os, const label maxLen) const
 {
-    label n = 0;
-
-    topoSet::const_iterator iter = this->cbegin();
+    labelHashSet::const_iterator iter = labelHashSet::cbegin();
 
     if (size() <= maxLen)
     {
-        writeDebug(os, maxLen, iter, n);
+        writeDebug(os, maxLen, iter);
     }
     else
     {
-        label halfLen = maxLen/2;
+        const label halfLen = maxLen/2;
 
         os  << "Size larger than " << maxLen << ". Printing first and last "
             << halfLen << " elements:" << nl << endl;
 
-        writeDebug(os, halfLen, iter, n);
+        label n = writeDebug(os, halfLen, iter);
 
         os  << nl << "  .." << nl << endl;
 
@@ -633,7 +680,7 @@ void Foam::topoSet::writeDebug(Ostream& os, const label maxLen) const
             ++iter;
         }
 
-        writeDebug(os, halfLen, iter, n);
+        writeDebug(os, halfLen, iter);
     }
 }
 
diff --git a/src/meshTools/topoSet/topoSets/topoSet.H b/src/meshTools/topoSet/topoSets/topoSet.H
index d843714966..5f424112b4 100644
--- a/src/meshTools/topoSet/topoSets/topoSet.H
+++ b/src/meshTools/topoSet/topoSets/topoSet.H
@@ -70,6 +70,15 @@ protected:
 
     // Protected Member Functions
 
+        //- Read into labelHashSet if IOobject flags set. Return true if read.
+        bool readIOcontents(const word& wantedType, labelHashSet& contents);
+
+        //- Check limits on addressable range.
+        void checkLabels(const labelUList& labels, const label maxSize);
+
+        //- Check limits on addressable range.
+        void checkLabels(const labelHashSet& labels, const label maxSize);
+
         //- Update map from map.
         //  Used to update cell/face labels after morphing
         virtual void updateLabels(const labelUList& map);
@@ -77,24 +86,25 @@ protected:
         //- Check limits on addressable range.
         virtual void check(const label maxSize);
 
-        //- Write part of contents nicely formatted. Prints labels only.
-        void writeDebug
+        //- Write part of contents nicely formatted.
+        //  Prints labels only.
+        //  \returns number of labels written
+        label writeDebug
         (
             Ostream& os,
             const label maxElem,
-            topoSet::const_iterator& iter,
-            label& elemI
+            labelHashSet::const_iterator& iter
         ) const;
 
-        //- Write part of contents nicely formatted. Prints label
-        //  and corresponding coordinate.
-        void writeDebug
+        //- Write part of contents nicely formatted.
+        //  Prints label and corresponding coordinate.
+        //  \returns number of labels written
+        label writeDebug
         (
             Ostream& os,
             const pointField& coords,
             const label maxElem,
-            topoSet::const_iterator& iter,
-            label& elemI
+            labelHashSet::const_iterator& iter
         ) const;
 
         //- Write labels and coordinates columnwise to os. Truncate to maxLen.
@@ -123,22 +133,37 @@ public:
         //- Name of file set will use.
         static fileName localPath(const polyMesh& mesh, const word& name);
 
-        //- Find IOobject in the polyMesh/sets (used as constructor helper)
+        //- Find IOobject in the polyMesh/sets/ (used as constructor helper)
         static IOobject findIOobject
         (
             const polyMesh& mesh,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Find IOobject in the polyMesh/sets (used as constructor helper)
+        //- Find IOobject in the polyMesh/sets/ (used as constructor helper)
+        static IOobject findIOobject
+        (
+            const polyMesh& mesh,
+            const word& name,
+            IOobjectOption::registerOption reg,
+            IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+        )
+        {
+            return findIOobject(mesh, name, rOpt, wOpt, reg);
+        }
+
+        //- Find IOobject in the polyMesh/sets/ (used as constructor helper)
         static IOobject findIOobject
         (
             const Time& runTime,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
 
@@ -196,6 +221,21 @@ public:
         //  Can't use typeName info here since subclasses not yet instantiated
         topoSet(const IOobject& io, const word& wantedType);
 
+        //- Construct empty (no-read) with IOobject information
+        topoSet(const IOobject& io, const Foam::zero);
+
+        //- Construct empty (no-read) with initial labelHashSet capacity,
+        //- with IOobject information
+        topoSet(const IOobject& io, const label initialCapacity);
+
+        //- Copy construct (no-read) from labelHashSet,
+        //- with IOobject information.
+        topoSet(const IOobject& io, const labelHashSet& labels);
+
+        //- Move construct (no-read) from labelHashSet,
+        //- with IOobject information.
+        topoSet(const IOobject& io, labelHashSet&& labels);
+
         //- Construct from polyMesh and name.
         //  Searches for a polyMesh/sets directory but not beyond the
         //  mesh.facesInstance().
@@ -205,21 +245,23 @@ public:
             const word& wantedType,
             const word& name,
             IOobjectOption::readOption rOpt = IOobjectOption::MUST_READ,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct empty from additional size of labelHashSet.
+        //- Construct empty (no-read) with initial labelHashSet capacity.
         //  Searches for a polyMesh/sets directory but not beyond the
         //  mesh.facesInstance().
         topoSet
         (
             const polyMesh& mesh,
             const word& name,
-            const label size,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            const label initialCapacity,
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct (no-read) with copy of labelHashSet
+        //- Copy construct (no-read) from labelHashSet.
         //  Searches for a polyMesh/sets directory but not beyond the
         //  mesh.facesInstance().
         topoSet
@@ -227,10 +269,11 @@ public:
             const polyMesh& mesh,
             const word& name,
             const labelHashSet& labels,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct (no-read) with moving labelHashSet
+        //- Move construct (no-read) from labelHashSet.
         //  Searches for a polyMesh/sets directory but not beyond the
         //  mesh.facesInstance().
         topoSet
@@ -238,10 +281,11 @@ public:
             const polyMesh& mesh,
             const word& name,
             labelHashSet&& labels,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct (no-read) with copy of labels
+        //- Copy construct (no-read) from list of labels.
         //  Searches for a polyMesh/sets directory but not beyond the
         //  mesh.facesInstance().
         topoSet
@@ -249,18 +293,10 @@ public:
             const polyMesh& mesh,
             const word& name,
             const labelUList& labels,
-            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE
+            IOobjectOption::writeOption wOpt = IOobjectOption::NO_WRITE,
+            IOobjectOption::registerOption reg = IOobjectOption::LEGACY_REGISTER
         );
 
-        //- Construct empty from IOobject and HashSet size.
-        topoSet(const IOobject& io, const label size);
-
-        //- Construct from IOobject and copy of labelHashSet.
-        topoSet(const IOobject& io, const labelHashSet& labels);
-
-        //- Construct from IOobject and move labelHashSet.
-        topoSet(const IOobject& io, labelHashSet&& labels);
-
 
         //- Clone
         autoPtr<topoSet> clone() const
@@ -309,6 +345,9 @@ public:
 
     // Member Functions
 
+        //- Has the given index?
+        virtual bool contains(const label id) const;
+
         //- Has the given index?
         virtual bool found(const label id) const;
 
@@ -329,23 +368,23 @@ public:
         virtual void invert(const label maxLen);
 
         //- Subset contents. Only elements present in both sets remain.
-        virtual void subset(const topoSet& set);
+        virtual void subset(const labelUList& elems);
 
         //- Subset contents. Only elements present in both sets remain.
-        virtual void subset(const labelUList& set);
+        virtual void subset(const topoSet& set);
 
-        //- Add elements
+        //- Add given elements to the set
+        virtual void addSet(const labelUList& elems);
+
+        //- Add given elements to the set
         virtual void addSet(const topoSet& set);
 
-        //- Add elements
-        virtual void addSet(const labelUList& set);
+        //- Subtract given elements from the set
+        virtual void subtractSet(const labelUList& elems);
 
-        //- Subtract elements
+        //- Subtract given elements from the set
         virtual void subtractSet(const topoSet& set);
 
-        //- Subtract elements
-        virtual void subtractSet(const labelUList& set);
-
 
         //- Sync set across coupled patches.
         virtual void sync(const polyMesh& mesh);
@@ -374,19 +413,23 @@ public:
         //- Return max allowable index (+1). Not implemented.
         virtual label maxSize(const polyMesh& mesh) const = 0;
 
-        //- Helper: call updateMesh on all sets in container (and
-        //  updates instance)
+        //- Helper: call updateMesh on all items in container
+        //- (and updates instance)
         template<class Container>
         static void updateMesh
         (
             const fileName& instance,
             const mapPolyMesh&,
-            Container&
+            Container& items
         );
 
-        //- Helper: set instance on all sets in container
+        //- Helper: set instance on all items in container
         template<class Container>
-        static void setInstance(const fileName& instance, Container&);
+        static void setInstance
+        (
+            const fileName& instance,
+            Container& items
+        );
 
         //- Helper: remove all sets files from mesh instance
         static void removeFiles(const polyMesh&);
diff --git a/src/meshTools/topoSet/topoSets/topoSetTemplates.C b/src/meshTools/topoSet/topoSets/topoSetTemplates.C
index d163d2e1a3..02e501f5d0 100644
--- a/src/meshTools/topoSet/topoSets/topoSetTemplates.C
+++ b/src/meshTools/topoSet/topoSets/topoSetTemplates.C
@@ -25,19 +25,18 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 template<class Container>
 void Foam::topoSet::setInstance
 (
     const fileName& instance,
-    Container& lst
+    Container& items
 )
 {
-    forAll(lst, i)
+    for (auto& item : items)
     {
-        lst[i].instance() = instance;
+        item.instance() = instance;
     }
 }
 
@@ -47,13 +46,13 @@ void Foam::topoSet::updateMesh
 (
     const fileName& instance,
     const mapPolyMesh& map,
-    Container& lst
+    Container& items
 )
 {
-    forAll(lst, i)
+    for (auto& item : items)
     {
-        lst[i].instance() = instance;
-        lst[i].updateMesh(map);
+        item.instance() = instance;
+        item.updateMesh(map);
     }
 }
 
diff --git a/src/overset/regionsToCell/regionsToCell.C b/src/overset/regionsToCell/regionsToCell.C
index 996743d394..af36c7fe3e 100644
--- a/src/overset/regionsToCell/regionsToCell.C
+++ b/src/overset/regionsToCell/regionsToCell.C
@@ -377,14 +377,16 @@ void Foam::regionsToCell::combine(topoSet& set, const bool add) const
     // Note: wip. Select cells first
     boolList selectedCell(mesh_.nCells(), true);
 
-    if (setName_.size() && setName_ != "none")
+    if (!setName_.empty() && setName_ != "none")
     {
-        Info<< "    Loading subset " << setName_ << " to delimit search region."
-            << endl;
-        cellSet subSet(mesh_, setName_);
+        Info<< "    Loading subset " << setName_
+            << " to delimit search region." << nl;
+
+        cellSet loadedSet(mesh_, setName_, IOobject::NO_REGISTER);
+        const labelHashSet& cellLabels = loadedSet;
 
         selectedCell = false;
-        for (const label celli : static_cast<const labelHashSet&>(subSet))
+        for (const label celli : cellLabels)
         {
             selectedCell[celli] = true;
         }