diff --git a/NEWS.md b/NEWS.md
index 8fe85a9..5f6bab6 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -6,6 +6,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## Unreleased
 
+### Added
+- Missing distributed functions. Since PR [#92](https://github.com/gridap/GridapEmbedded.jl/pull/92).
+- Background models extended with remote ghosts inherit Cartesian labels. Since PR [#93](https://github.com/gridap/GridapEmbedded.jl/pull/93).
+
 ### Fixed
 - Unused `name` keywork argument in `square` and `quadrilateral` analytical geometries. Since PR [#86](https://github.com/gridap/GridapEmbedded.jl/pull/86).
 - Gluing of the remote root cells to the local+ghost mesh. Since PR [#91](https://github.com/gridap/GridapEmbedded.jl/pull/91).
diff --git a/Project.toml b/Project.toml
index 0b74b84..5ccc378 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "GridapEmbedded"
 uuid = "8838a6a3-0006-4405-b874-385995508d5d"
 authors = ["Francesc Verdugo <f.verdugo.rojano@vu.nl>", "Eric Neiva <eric.neiva@college-de-france.fr>", "Pere Antoni Martorell <pere.antoni.martorell@upc.edu>", "Santiago Badia <santiago.badia@monash.edu>"]
-version = "0.9.3"
+version = "0.9.4"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
diff --git a/src/Distributed/DistributedAgFEM.jl b/src/Distributed/DistributedAgFEM.jl
index 89c6ab2..4501ba7 100644
--- a/src/Distributed/DistributedAgFEM.jl
+++ b/src/Distributed/DistributedAgFEM.jl
@@ -371,10 +371,61 @@ function add_remote_cells(model::DistributedDiscreteModel,remote_cells,remote_pa
 
   # Build appended model
   lgrids = map(get_grid,local_views(model))
-  grids = map(lazy_append,lgrids,rgrids)
-  models = map(UnstructuredDiscreteModel,grids)
+  _grids = map(lazy_append,lgrids,rgrids)
+  _models = map(UnstructuredDiscreteModel,_grids)
   agids = add_remote_ids(gids,remote_cells,remote_parts)
-  DistributedDiscreteModel(models,agids) |> merge_nodes
+  amodel = DistributedDiscreteModel(_models,agids) |> merge_nodes
+
+  D = num_cell_dims(model)
+  grids = map(get_grid,local_views(amodel))
+  topos = map(get_grid_topology,local_views(amodel))
+  d_to_dface_to_entity = map(topos) do topo
+    [ fill(Int32(UNSET),num_faces(topo,d)) for d in 0:D ]
+  end
+  oldtopos = map(get_grid_topology,local_views(model))
+  oldlabels = map(get_face_labeling,local_views(model))
+  for d in 0:D
+    _fill_labels!(d_to_dface_to_entity,
+                  oldlabels,
+                  oldtopos,
+                  topos,
+                  ncells,
+                  d,D,
+                  snd_lids,
+                  rgraph)
+  end
+  labels = map(d_to_dface_to_entity,oldlabels) do d_to_dface_to_entity,ol
+    FaceLabeling(d_to_dface_to_entity,ol.tag_to_entities,ol.tag_to_name)
+  end
+  models = map(UnstructuredDiscreteModel,grids,topos,labels)
+  DistributedDiscreteModel(models,agids)
+end
+
+function _fill_labels!(d_to_dface_to_entity,llabels,ltopos,ntopos,nremotes,
+                       d::Int,D::Int,snd_lids,rgraph)
+  snd_labels = map(ltopos,llabels,snd_lids) do topo,labels,lids
+    dface_to_entity = get_face_entity(labels,d)
+    T = eltype(eltype(dface_to_entity))
+    labels = map(lids) do lids
+      faces = map(Reindex(get_faces(topo,D,d)),lids)
+      labels = map(Reindex(dface_to_entity),faces)
+      reduce(append!,labels,init=T[])
+    end
+    Vector{Vector{T}}(labels)
+  end
+  rcv_labels = allocate_exchange(snd_labels,rgraph)
+  exchange!(rcv_labels,snd_labels,rgraph) |> wait
+  rlabels = map(PartitionedArrays.getdata,rcv_labels)
+  map(d_to_dface_to_entity,llabels) do d_to_dface_to_entity,l
+    l_face_entity = get_face_entity(l,d)
+    d_to_dface_to_entity[d+1][1:length(l_face_entity)] = l_face_entity
+  end
+  map(d_to_dface_to_entity,ntopos,nremotes,rlabels) do d_to_dface_to_entity,nt,nr,r
+    nr > 0 && begin
+      rf = reduce(vcat,get_faces(nt,D,d)[end-nr+1:end])
+      d_to_dface_to_entity[d+1][rf] = r
+    end
+  end
 end
 
 function add_remote_aggregates(model::DistributedDiscreteModel,aggregates,aggregate_owner)