  Random sequential adsorption (RSA) models have been studied 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 to 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**0.5 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/(k-1)]. In the case of RSA
of lattice hard squares in 2D with diffusional relaxation the approach to the
full coverage is ~t**(-0.5).
