Before revision:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as  in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
After revision:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as the generalization of this property in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .