  To study the effect of quenched disorder in a class of reaction-diffusion
systems, we introduce a conserved mass model of diffusion and aggregation in
which the mass moves as a whole to a nearest neighbour on most sites while it
fragments off as a single monomer (i.e. chips off) from certain fixed sites.
Once the mass leaves any site, it coalesces with the mass present on its
neighbour. We study in detail the effect of a \emph{single} chipping site on
the steady state in arbitrary dimensions, with and without bias. In the
thermodynamic limit, the system can exist in one of the following phases -- (a)
Pinned Aggregate (PA) phase in which an infinite aggregate (with mass
proportional to the volume of the system) appears with probability one at the
chipping site but not in the bulk. (b) Unpinned Aggregate (UA) phase in which
$\emph{both}$ the chipping site and the bulk can support an infinite aggregate
simultaneously. (c) Non Aggregate (NA) phase in which there is no infinite
cluster. Our analytical and numerical studies show that the system exists in
the UA phase in all cases except in 1d with bias. In the latter case, there is
a phase transition from the NA phase to the PA phase as density is increased. A
variant of the above aggregation model is also considered in which total
particle number is conserved and chipping occurs at a fixed site, but the
particles do not interact with each other at other sites. This model is solved
exactly by mapping it to a Zero Range Process. With increasing density, it
exhibits a phase transition from the NA phase to the PA phase in all
dimensions, irrespective of bias. Finally, we discuss the likely behaviour of
the system in the presence of extensive disorder.
