  We study nonequilibrium phase transitions of reaction-diffusion systems
defined on randomly diluted lattices, focusing on the transition across the
lattice percolation threshold. To develop a theory for this transition, we
combine classical percolation theory with the properties of the supercritical
nonequilibrium system on a finite-size cluster. In the case of the contact
process, the interplay between geometric criticality due to percolation and
dynamical fluctuations of the nonequilibrium system leads to a new universality
class. The critical point is characterized by ultraslow activated dynamical
scaling and accompanied by strong Griffiths singularities. To confirm the
universality of this exotic scaling scenario we also study the generalized
contact process with several (symmetric) absorbing states, and we support our
theory by extensive Monte-Carlo simulations.
