  We consider a continuous-time random walk on a regular tree of finite depth
and study its favorite points among the leaf vertices. For the walk started
from a leaf vertex and stopped upon hitting the root we prove that, in the
limit as as the depth of the tree tends to infinity, the suitably scaled and
centered maximal time spent at any leaf converges to a randomly-shifted Gumbel
law. The random shift is characterized using a derivative-martingale like
object associated with square-root local-time process on the tree.
