  The capture numbers entering the rate equations (RE) for submonolayer film
growth are determined from extensive kinetic Monte Carlo (KMC) simulations for
simple representative growth models yielding point, compact, and fractal island
morphologies. The full dependence of the capture numbers on island size, and on
both the coverage and the D/F ratio between the adatom diffusion coefficient D
and deposition rate F is determined. Based on this information, the RE are
solved to give the RE island size distribution (RE-ISD). The RE-ISDs are shown
to agree well with the corresponding KMC-ISDs for all island morphologies. For
compact morphologies, however, this agreement is only present for coverages
smaller than about 5% due to a significantly increased coalescence rate
compared to fractal morphologies. As found earlier, the scaled KMC-ISDs as a
function of scaled island size approach, for fixed coverage, a limiting curve
for D/F going to infinity. Our findings provide evidence that the limiting
curve is independent of the coverage for point islands, while the results for
compact and fractal island morphologies indicate a dependence on the coverage.
