A minimal model for molecular-beam-epitaxy in the submonolayer at room temperature is investigated by simulations and analytically. Aggregation of diffusing monomers leads to immobile islands which further grow by absorbing deposited and diffusing atoms. In the intermediate stage of growth, islands assume a fractal shape similar to diffusion-limited-aggregates. It is shown that the maximum density of islands in the submonolayer decreases approximately as a 1/3-power of the beam intensity F, in agreement with a prediction based on rate equations. A detailed analysis of adatom-adatom and adatom-island collisions explains some discrepancies between simulation data and simple rate-equation results.