  We study the dynamical properties of a collection of models for communication
processes, characterized by a single parameter $\xi$ representing the relation
between information load of the nodes and its ability to deliver this
information. The critical transition to congestion reported so far occurs only
for $\xi=1$. This case is well analyzed for different network topologies. We
focus of the properties of the order parameter, the susceptibility and the time
correlations when approaching the critical point. For $\xi<1$ no transition to
congestion is observed but it remains a cross-over from a low-density to a
high-density state. For $\xi>1$ the transition to congestion is discontinuous
and congestion nuclei arise.
