  The aim of this note is to extend the result of Angel and Holroyd concerning
the transience and the recurrence of transfinite rotor-router walks, for random
initial configuration of rotors on homogeneous trees. We address the same
question on directed covers of finite graphs, which are also called trees with
finitely many cone types or periodic trees. Furthermore, we provide an example
of a directed cover such that the rotor-router walk can be either recurrent or
transient, depending only on the planar embedding of the periodic tree.
