Xiong proved that if / : / -> / is any map of the unit interval /, then the depth of the centre of / is at most 2, and Ye proved that for any map / : T ->• T of a finite tree T, the depth of the centre of / is at most 3. It is natural to ask whether the result can be generalized to maps of dendrites. In this note, we show that there is a dendrite D such that for any countable ordinal number X there is a map / : D -> D such that the depth of centre of / is k. As a corollary, we show that for any countable ordinal number X there is a map (respectively a homeomorphism) / of a 2-dimensional ball B 2 (respectively a 3-dimensional ball 5 3 ) such that the depth of centre of / is A.1991 Mathematics subject classification (Amer. Math. Soc): primary 54H20; secondary 58F50.