diff --git a/applications/test/globalIndex/Test-globalIndex.C b/applications/test/globalIndex/Test-globalIndex.C
index 88a6d4d695..bb436561b0 100644
--- a/applications/test/globalIndex/Test-globalIndex.C
+++ b/applications/test/globalIndex/Test-globalIndex.C
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -92,6 +93,11 @@ int main(int argc, char *argv[])
     }
 
 
+    Info<< "Max number of cells: " << globalNumbering.maxSize() << nl;
+    Pout<< "nCells: "
+        << globalNumbering.localSize() << " Max off-processor: "
+        << globalNumbering.maxNonLocalSize() << nl;
+
     // Try whichProcID on a few borderline cases.
 
     if (mesh.nCells() < 1)
diff --git a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.C b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.C
index 93a33346e5..957725dee6 100644
--- a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.C
+++ b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -159,6 +159,30 @@ Foam::labelList Foam::globalIndex::sizes() const
 }
 
 
+Foam::label Foam::globalIndex::maxNonLocalSize(const label proci) const
+{
+    const label len = (offsets_.size() - 1);
+
+    if (len < 1)
+    {
+        return 0;
+    }
+
+    label maxLen = 0;
+
+    for (label i=0; i < len; ++i)
+    {
+        if (i != proci)
+        {
+            const label localLen = (offsets_[i+1] - offsets_[i]);
+            maxLen = max(maxLen, localLen);
+        }
+    }
+
+    return maxLen;
+}
+
+
 // * * * * * * * * * * * * * * * Friend Operators  * * * * * * * * * * * * * //
 
 Foam::Istream& Foam::operator>>(Istream& is, globalIndex& gi)
diff --git a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.H b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.H
index 45fbcdb25a..9059d2aa17 100644
--- a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.H
+++ b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndex.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2019 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -53,7 +53,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declarations
+// Forward Declarations
 
 class globalIndex;
 class labelRange;
@@ -81,7 +81,7 @@ class globalIndex
         );
 
 
-    // Private data
+    // Private Data
 
         //- Start of proci. Size is nProcs()+1. (so like CompactListList)
         labelList offsets_;
@@ -91,7 +91,7 @@ public:
 
     // Constructors
 
-        //- Construct null
+        //- Default construct
         globalIndex() = default;
 
         //- Construct from local max size.
@@ -120,23 +120,26 @@ public:
 
     // Member Functions
 
-        //- Check for null constructed or global sum == 0
+        //- Check for default constructed or global sum == 0
         inline bool empty() const;
 
-        //- Const-access to the offsets
-        inline const labelList& offsets() const;
-
         //- Global sum of localSizes
         inline label size() const;
 
         //- The local sizes
         labelList sizes() const;
 
+        //- Global max of localSizes
+        inline label maxSize() const;
+
+        //- Const-access to the offsets
+        inline const labelList& offsets() const noexcept;
+
 
     // Edit
 
         //- Write-access to the offsets, for changing after construction
-        inline labelList& offsets();
+        inline labelList& offsets() noexcept;
 
         //- Reset from local size.
         //  Does communication with default communicator and message tag.
@@ -153,6 +156,8 @@ public:
         );
 
 
+        // Queries
+
         // Queries relating to my processor (using world communicator)
 
             //- My local start
@@ -161,6 +166,9 @@ public:
             //- My local size
             inline label localSize() const;
 
+            //- The max of localSizes, excluding current processor
+            inline label maxNonLocalSize() const;
+
             //- Return start/size range of local processor data
             inline labelRange range() const;
 
@@ -181,7 +189,7 @@ public:
             inline label toLocal(const label i) const;
 
 
-        // Global queries
+        // Global (off-processor) queries
 
             //- Start of proci data
             inline label offset(const label proci) const;
@@ -192,6 +200,9 @@ public:
             //- Size of proci data
             inline label localSize(const label proci) const;
 
+            //- The max of localSizes, excluding the specified processor
+            label maxNonLocalSize(const label proci) const;
+
             //- Return start/size range of proci data
             inline labelRange range(const label proci) const;
 
diff --git a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndexI.H b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndexI.H
index 04e51697b0..7dea5118a4 100644
--- a/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndexI.H
+++ b/src/OpenFOAM/meshes/polyMesh/globalMeshData/globalIndexI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2021 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -73,13 +73,13 @@ inline bool Foam::globalIndex::empty() const
 }
 
 
-inline const Foam::labelList& Foam::globalIndex::offsets() const
+inline const Foam::labelList& Foam::globalIndex::offsets() const noexcept
 {
     return offsets_;
 }
 
 
-inline Foam::labelList& Foam::globalIndex::offsets()
+inline Foam::labelList& Foam::globalIndex::offsets() noexcept
 {
     return offsets_;
 }
@@ -127,6 +127,19 @@ inline Foam::label Foam::globalIndex::localSize() const
 }
 
 
+inline Foam::label Foam::globalIndex::maxSize() const
+{
+    // Use out-of-range proci to avoid excluding any processor
+    return maxNonLocalSize(-1);
+}
+
+
+inline Foam::label Foam::globalIndex::maxNonLocalSize() const
+{
+    return maxNonLocalSize(Pstream::myProcNo());
+}
+
+
 inline Foam::labelRange Foam::globalIndex::range(const label proci) const
 {
     return labelRange(offsets_[proci], offsets_[proci+1] - offsets_[proci]);