  We investigate submonolayer epitaxial growth with a fixed monomer flux and
irreversible aggregation of adatom islands due to their effective diffusion.
When the diffusivity D_k of an island of mass k is proportional to k^{-\mu}, a
Smoluchowski rate equation approach predicts steady behavior for 0<\mu<1, with
the concentration c_k of islands of mass k varying as k^{-(3-\mu)/2}. For
\mu>1, continuous evolution occurs in which c_k(t)~(\ln t)^{-(2k-1)\mu/2},
while the total island density increases as N(t)~(\ln t)^{\mu/2}. Monte Carlo
simulations support these predictions.
