InAs islands have been grown by gas source molecular beam epitaxy on (1 1 3)B InP substrates and examined by atomic force microscopy and photoluminescence. Two types of island size and spatial distribution have been identified. For deposits lower than 2.4 monolayers, an almost linear increase of density of islands presenting a nearly constant size is observed. For higher InAs coverages which correspond to the formation of extremely dense island arrays, a saturation of density occurs and island size decreases. It is suggested that the constant size at low coverage is related to self-limiting island growth and that the island density saturation at higher coverage is mainly due to long range interactions through the substrate.