Kinetics of deposition in the diffusion-controlled limit

The adsorption of particles diffusing in a half space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the three-dimensional half space, the coverage approaches its saturated "jamming" value as t^{-1} in the large time limit (generally as t^{-1/(d-1)} when the substrate is d dimensional and d>1, and as e^{-t/ln(t)} when d=1). We also analyze the asymptotic behavior when particles are spherical and when particles are planar aligned squares.