  We present a simple model of communication in networks with hierarchical
branching. We analyze the behavior of the model from the viewpoint of critical
systems under different situations. For certain values of the parameters, a
continuous phase transition between a sparse and a congested regime is observed
and accurately described by an order parameter and the power spectra. At the
critical point the behavior of the model is totally independent of the number
of hierarchical levels. Also scaling properties are observed when the size of
the system varies. The presence of noise in the communication is shown to break
the transition. Despite the simplicity of the model, the analytical results are
a useful guide to forecast the main features of real networks.
