  We study the effect of the presence of a regular substrate pattern on the
irreversible adsorption of nanosized and colloid particles. Deposition of disks
of radius $r_0$ is considered, with the allowed regions for their center
attachment at the planar surface consisting of square cells arranged in a
square lattice pattern. We study the jammed state properties of a generalized
version of the random sequential adsorption model for different values of the
cell size, $a$, and cell-cell separation, $b$. The model shows a surprisingly
rich behavior in the space of the two dimensionless parameters $\alpha=a/2r_0$
and $\beta=b/2r_0$. Extensive Monte Carlo simulations for system sizes of
$500\times500$ square lattice unit cells were performed by utilizing an
efficient algorithm, to characterize the jammed state morphology.
