  We give a comprehensive rate equation description for the irreversible growth
of aggregates by migration from small to large aggregates. For a homogeneous
rate K(i;j) at which monomers migrate from aggregates of size i to those of
size j, that is, K(ai;aj) ~ a^{lambda} K(i,j), the mean aggregate size grows
with time as t^{1/(2-lambda)} for lambda<2. The aggregate size distribution
exhibits distinct regimes of behavior which are controlled by the scaling
properties of the migration rate from the smallest to the largest aggregates.
Our theory applies to diverse phenomena, such as the distribution of city
populations, late stage coarsening of non-symmetric binary systems, and models
for wealth exchange.
