  We study biased random walk on subcritical and supercritical Galton-Watson
trees conditioned to survive in the transient, sub-ballistic regime. By
considering offspring laws with infinite variance, we extend previously known
results for the walk on the supercritical tree and observe new trapping
phenomena for the walk on the subcritical tree which, in this case, always
yield sub-ballisticity. This is contrary to the walk on the supercritical tree
which always has some ballistic phase.
