  Mother groups are the basic building blocks for polynomial automaton groups.
We show that, in contrast with mother groups of degree 0 or 1, any bounded,
symmetric, generating random walk on the mother groups of degree at least 3 has
positive speed. The proof is based on an analysis of resistance in fractal
mother graphs. We give upper bounds on resistances in these graphs, and show
that infinite versions are tran- sient.
