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There exist several methods of computing an automaton recognizing the language denoted by a given regular expression: In the case of words, the position automaton P due to Glushkov, the c-continuation automaton C due to Champarnaud and Ziadi, the follow automaton F due to Ilie and Yu and the equation automaton ε due to Antimirov. It has been shown that P and C are isomorphic and that ε (resp. F) is a quotient of C (resp. of P). In this paper, we define from a given regular tree expression the position tree automaton P and the follow tree automaton F. Using the definition of the equation tree automaton ε of Kuske and Meinecke and our previously defined c-continuation tree automaton C, we show that the previous morphic relations are still valid on tree expressions. [ABSTRACT FROM AUTHOR]