  We study the asymmetric exclusion process on a regular Cayley tree with
arbitrary co-ordination number. In this model particles can enter the system
only at the parent site and exit from one of the sites at the last level. In
the bulk they move from the occupied sites to one of their unoccupied downward
neighbours, chosen randomly. We show that the steady state current that flow
from one level to the next is independent of the exit rate, and increase
monotonically with the entry rate and the co-ordination number. Unlike TASEP,
the model has only one phase and the density profile show no boundary layers.
We argue that in blood, air or water circulations systems branching is
essential to maintain a free flow within the system which is independent of
exit rates.
