AbstractRandom sequential adsorption (RSA) models have been studied [1] due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard‐core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated; in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case of the power law behavior in the continuum deposition. 2D lattice and continuum simulations rule out some “exact” conjectures for the jamming coverage. For the deposition of dimers on a 1D lattice with diffusional relaxation we find that the limiting coverage (100%) is approached according to the ∼1/√t power‐law preceded, for fast diffusion, by the mean‐field crossover regime with the intermediate ∼1/t behavior. In case of k‐mer deposition (k>3) with diffusion the void fraction decreases according to the power‐law t−1/2. In the case of RSA of lattice hard squares in 2D with diffusional relaxation the approach to the full coverage is ∼t−1/2. In case of RSA‐deposition with diffusion of two by two square objects on a 2D square lattice the coverage also approaches 1 according to the power law t−1/2, while on a finite periodic lattice the final state is a frozen random regular grid of domain walls connecting single site defects.