Models where pairs, triples, or larger (typically connected) sets of sites on a 2Dlattice ‘‘fill’’ irreversibly (described here as dimer, trimer, ... filling or adsorption),either randomly or cooperatively, are required to describe many surfaceadsorption and reaction processes. Since filling is assumed to be irreversible and immobile (species are ‘‘frozen’’ once adsorbed), even the stationary, saturation state, which is nontrivial since the lattice cannot fill completely, is not in equilibrium. The kinetics and statistics of these processes are naturally described by recasting the master equations in hierarchic form for probabilities of subconfigurations of empty sites. These hierarchies are infinite for the infinite lattices considered here, but approximate solutions can be obtained by implementing truncation procedures. Those used here exploit a shielding property of suitable walls of empty sites peculiar to irreversible filling processes. Accurate results, including saturation coverage estimates, are presented for random filling of dimers, and trimers of different shapes, on various infinite 2Dlattices, and for square tetramers on an infinite square lattice.