  We consider the motion of a particle on a Galton Watson tree, when the
probabilities of jumping from a vertex to any one of its neighbours is
determined by a random process. Given the tree, positive weights are assigned
to the edges in such a way that, viewed along any line of descent, they evolve
as a random process. In order to introduce our method for proving transience or
recurrence, we first suppose that the weights are i.i.d., reproving a result of
Lyons and Pemantle. We then extend the argument to allow a Markovian
environment, and finally to a random walk on a Markovian environment that
changes the environment. Our approach involves studying the typical behaviour
of processes on fixed lines of descent, which we then show determines the
behaviour of the process on the whole tree.
