Multicluster growth via irreversible cooperative filling on lattices

Consider irreversible cooperative filling of sites on an infinite lattice where the filling rates $k_i$ depend on the number, i, of occupied sites adjacent to the site(s) being filled. If clustering is significantly enhanced relative to nucleation ($k_1$/$k_0$≡ρ≫1), then the process is thought of as a competition between nucleation, growth, and (possible) coalescence of clusters. These could be Eden clusters with or without permanent voids, Eden trees, or have modified but compact structure (depending on the $k_i$, i≥1).