Branching trees

p = 0.9;
maxdepth = 4;
tree[n_, f_] := (If[Length[Flatten[n]] > maxdepth, {},
    If[Or[RandomReal[] < p, Length[Flatten[n]] < 2],
     Table[{n -> {n, i}, tree[{n, i}, f]}, {i, f}], {}]]);
tree[k_] :=
  Map[FromDigits[Flatten@#[[1]], k] ->
     FromDigits[Flatten@#[[2]], k] &, Flatten[tree[{0}, k]]];
t = tree[3];
GraphPlot[Flatten[t]]