diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py
index ccfca8c36..2d94eee9f 100644
--- a/src/underworld3/discretisation/discretisation_mesh.py
+++ b/src/underworld3/discretisation/discretisation_mesh.py
@@ -1933,8 +1933,9 @@ def _surviving_labels(self, subdm, candidates):
         Returns
         -------
         dict
-            The subset of ``candidates`` present on ``subdm`` with a
-            non-empty stratum, preserving candidate order.
+            Candidates with a non-empty stratum anywhere on the DM communicator,
+            preserving candidate order. Empty ranks retain the same names and
+            empty labels, so solver boundary registration is rank independent.
         """
         present = set()
         for i in range(subdm.getNumLabels()):
@@ -1961,6 +1962,14 @@ def _surviving_labels(self, subdm, candidates):
             lsis = lab.getStratumIS(value)
             if lsis is not None and lsis.getSize() > 0:
                 present.add(name)
+        # A boundary may be absent from this rank while present on its peers.
+        # Its enum and label must nevertheless exist everywhere: natural BC
+        # registration and solver setup use the same named boundaries on all ranks.
+        present = set().union(*subdm.comm.tompi4py().allgather(present))
+        local_names = {subdm.getLabelName(i) for i in range(subdm.getNumLabels())}
+        for name in candidates:
+            if name in present and name not in local_names:
+                subdm.createLabel(name)
         return {name: v for name, v in candidates.items() if name in present}
 
     def extract_region(self, label_name, label_value=None):
diff --git a/tests/parallel/test_1085_submesh_boundary_names.py b/tests/parallel/test_1085_submesh_boundary_names.py
new file mode 100644
index 000000000..a6795158d
--- /dev/null
+++ b/tests/parallel/test_1085_submesh_boundary_names.py
@@ -0,0 +1,31 @@
+"""Submesh boundary names must survive on ranks owning no boundary points."""
+
+from petsc4py import PETSc
+import underworld3 as uw
+
+
+def test_surviving_labels_use_global_presence_and_create_empty_local_labels():
+    dm = PETSc.DMPlex().createBoxMesh([2, 2], simplex=False, comm=uw.mpi.comm)
+    if uw.mpi.rank == 0:
+        dm.createLabel('OnlyOnZero')
+        dm.setLabelValue('OnlyOnZero', dm.getChart()[0], 42)
+    surviving = uw.discretisation.Mesh._surviving_labels(
+        None, dm, {'OnlyOnZero': 42, 'AbsentEverywhere': 99}
+    )
+    assert surviving == {'OnlyOnZero': 42}
+    assert dm.getLabel('OnlyOnZero') is not None
+    assert 'AbsentEverywhere' not in [dm.getLabelName(i) for i in range(dm.getNumLabels())]
+    if uw.mpi.rank > 0:
+        values = dm.getLabel('OnlyOnZero').getValueIS()
+        assert values is None or len(values.getIndices()) == 0
+    dm.destroy()
+
+
+def test_extracted_region_boundary_enums_are_identical_on_every_rank():
+    mesh = uw.meshing.BoxInternalBoundary(
+        elementRes=(12,12), zelementRes=(10,2), zintCoord=.85,
+        minCoords=(0.,0.), maxCoords=(1.,1.), simplex=True, qdegree=2)
+    child = mesh.extract_region('Outer')
+    names = [(b.name,b.value) for b in child.boundaries]
+    assert all(other == names for other in uw.mpi.comm.allgather(names))
+    assert 'Top' in dict(names)