  The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a
model of coagulation with single-particle break up is studied both analytically
and numerically. The model with alpha=0 is known to undergo a nonequilibrium
phase transition as the mass density in the system is varied from a phase with
an exponential distribution of mass to a phase with a power-law distribution of
masses in addition to a single infinite aggregate. This transition is shown to
be curbed, at finite densities, for all alpha > 0 in any dimension. However, a
signature of this transition is seen in finite systems in the form of a large
aggregate and the finite size scaling implications of this are characterized.
The exponents characterizing the steady state probability that a randomly
chosen site has mass m are calculated using scaling arguments. The full
probability distribution is obtained within a mean field approximation and
found to compare well with the results from numerical simulations in one
dimension.
