Mathias,

this patch seems to work:

diff --git a/source/lac/trilinos_sparsity_pattern.cc 
b/source/lac/trilinos_sparsity_pattern.cc
index 84403175c6..c448279505 100644
--- a/source/lac/trilinos_sparsity_pattern.cc
+++ b/source/lac/trilinos_sparsity_pattern.cc
@@ -791,7 +791,8 @@ namespace TrilinosWrappers
     if (nonlocal_graph.get() != nullptr)
       {
         if (nonlocal_graph->IndicesAreGlobal() == false &&
-            nonlocal_graph->RowMap().NumMyElements() > 0)
+            nonlocal_graph->RowMap().NumMyElements() > 0 &&
+            column_space_map->NumMyElements() > 0)
           {
             // Insert dummy element at (row, column) that corresponds to 
row 0
             // in local index counting.
@@ -813,6 +814,7 @@ namespace TrilinosWrappers
             AssertThrow(ierr == 0, ExcTrilinosError(ierr));
           }
         Assert(nonlocal_graph->RowMap().NumMyElements() == 0 ||
+                 column_space_map->NumMyElements() == 0 ||
                  nonlocal_graph->IndicesAreGlobal() == true,
                ExcInternalError());
 
Still needs some testing, though.
Can you give it a a shot?

Best,
Daniel

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