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 as well as in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .