(* this is needed to cluster the largest layer 'L' in such a way that
it's compatible with the size of the second-largest layer 'l' *)

ClusterLargestLayer[L_, l_] := Module[{n, m, c, out},
   n = Length[L];
   m = Length[l];
   c = Floor[n/m];   (* cluster size *)

   out = Partition[Take[L, m c], c];
   out[[-1]] = Join[out[[-1]], Drop[L, m c]];

   out
   ];



(* this generates a tree from ls = {l,m,r} *)

Tree[ls_] := Module[{clusterSize, ls3},

   (* cluster largest layer *)
   ls3 = ClusterLargestLayer[ls[[3]], ls[[2]]];

   (* generate a tree using the above clustering *)
   Flatten[Table[{ls[[1, 1]], ls[[2, j]], #} & /@ ls3[[j]], {j, Length[ls[[2]]]}], 1]
   ];



(* show the tree, example use: ShowTree@Tree[{l,m,r}] *)

ShowTree[tree_] :=
  Graph[DirectedEdge @@ # & /@
    Flatten[Partition[#, 2, 1] & /@ tree, 1], VertexLabels -> "Name"];



(* the main function *)

FindMinimalPaths[list_] := Module[{l, m, r, paths},
   (* reorder from smallest to largest number of elements *)
   {l, m, r} = SortBy[list, Length];

   (* intialize *)
   paths = {};

   (* the main loops *)
   Do[
    Do[
     AppendTo[paths, #] & /@ Tree[{l, m, r}];    (* append the paths in 'tree' to 'paths' *)
     m = RotateLeft[m];    (* prepare for next inner iteration *)
     , {Ceiling[ Length[m]/Length[l] ]}];
    l = RotateLeft[l];    (* prepare for next outer iteration *)
    , {Length[l]}];


   (* output *)
   Sort /@ paths

   ];


FindMinimalPaths[{{a, b}, {c, d, e, f}, {X, Y, Z, W}}]