  We examine the island size distribution function and spatial correlation
function of a model for island growth in the submonolayer regime in both 1 and
2 dimensions. In our model the islands do not grow in shape, and a fixed number
of adatoms are added, nucleate, and are trapped at islands as they diffuse.
  We study the cases of various critical island sizes $i$ for nucleation as a
function of initial coverage. We found anomalous scaling of the island size
distribution for large $i$ . Using scaling, random walk theory, a version of
mean-field theory we obtain a closed form for the spatial correlation function.
Our analytic results are verified by Monte Carlo simulations.
