  Adding sand grains at a single site in Abelian sandpile models produces
beautiful but complex patterns. We study the effect of sink sites on such
patterns. Sinks change the scaling of the diameter of the pattern with the
number $N$ of sand grains added. For example, in two dimensions, in presence of
a sink site, the diameter of the pattern grows as $\sqrt{(N/\log N)}$ for large
$N$, whereas it grows as $\sqrt{N}$ if there are no sink sites. In presence of
a line of sink sites, this rate reduces to $N^{1/3}$. We determine the growth
rates for these sink geometries along with the case when there are two lines of
sink sites forming a wedge, and its generalization to higher dimensions. We
characterize one such asymptotic patterns on the two-dimensional F-lattice with
a single source adjacent to a line of sink sites, in terms of position of
different spatial features in the pattern. For this lattice, we also provide an
exact characterization of the pattern with two sources, when the line joining
them is along one of the axes.
