Phase transitions of reaction-diffusion systems with a site occupation restriction, particle creation requiring n > 2 parents, and in which explicit diffusion of single particles (A) is possible, are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of nonequilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some recent numerical analyses. Simulation results for one- and two-dimensional binary spreading model, 2A -> 4A, 4A -> 2A, reveal a new type of mean-field criticality characterized by the critical exponents a = 1/3 and b = 1/2, as suggested in a recent preprint [cond-mat/0210615]