A new description of the growth mechanism for the islands in submonolayer film coverage is presented which goes beyond the usual mean-field approximations. We show that the scaling behaviour observed during heterogeneous growth simulations is explained by the existence of capture zones for each island which remain unchanged throughout the evolution. These capture zones are in fact the Voronoi polygons for the island centres and so represent the departure of the local island environment from the average. The relevance and range of applicability of this description for homogeneous nucleation systems are discussed.