  We have numerically studied the trapping problem in a two-dimensional lattice
where particles are continuously generated. We have introduced interaction
between particles and directionality of their movement. This model presents a
critical behaviour with a rich phase structure similar to spin systems. We
interpret a change in the asymptotic density of particles as a phase
transition. For high directionality the change is abrupt, possibly of first
order. For small directionality the phase transition is of higher order. We
have computed the phase diagram, the volume dependence of the critical point,
and the relaxation time of the system in the large volume limit.
