  Phase transitions of reaction-diffusion systems with site occupation
restriction and with particle creation that requires n>1 parents and where
explicit diffusion of single particles (A) exists are reviewed. Arguments based
on mean-field approximation and simulations are given which support novel kind
of non-equilibrium criticality. These are in contradiction with the
implications of a suggested phenomenological, multiplicative noise Langevin
equation approach and with some of recent numerical analysis. Simulation
results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A
model display a new type of mean-field criticality characterized by alpha=1/3
and beta=1/2 critical exponents suggested in cond-mat/0210615.
