  We consider the DLA process on a cylinder G x N. It is shown that this
process "grows arms", provided that the base graph G has small enough mixing
time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the
time it takes the cluster to reach the m-th layer of the cylinder is at most of
order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs
of degree 5, for which the DLA cluster on these graphs has arbitrarily small
density.
  In addition, we provide an upper bound on the rate at which the "arms" grow.
This bound is valid for a large class of base graphs G, including discrete tori
of dimension at least 3.
  It is also shown that for any base graph G, the density of the DLA process on
a G-cylinder is related to the rate at which the arms of the cluster grow. This
implies, that for any vertex transitive G, the density of DLA on a G-cylinder
is bounded by 2/3.
