  We study the coherent transport modeled by continuous-time quantum walks,
focussing on hierarchical structures. For these we use Husimi cacti, lattices
dual to the dendrimers. We find that the transport depends strongly on the
initial site of the excitation. For systems of sizes $N\le21$, we find that
processes which start at central sites are nearly recurrent. Furthermore, we
compare the classical limiting probability distribution to the long time
average of the quantum mechanical transition probability which shows
characteristic patterns. We succeed in finding a good lower bound for the
(space) average of the quantum mechanical probability to be still or again at
the initial site.
