Growth of GaAs on (111) B substrates masked by Si3N4 was studied with the periodic supply epitaxy (PSE) technique using a molecular beam epitaxy system. The conditions for selectivity to occur were investigated, together with the influence of the As-4 overpressure on selectivity and on the morphology of the grown layer. It was found that an interruption time of 4 min was too short to allow for complete selective growth to take place, but it was sufficient to allow the formation of a depleted zone of 200-500 nm at the borders of the dielectric mask. Lateral overgrowth of the epitaxial layer was found possible in these partially selective conditions after 60 min of GaAs deposition in the PSE mode. The morphology of the ridges grown at different As-4 overpressures was studied. At higher As-4 pressures, the epitaxial layer grew without contact with the mask walls and developed independent {210} lateral sidewalls. The shrinkage rate of the top (111) B plane was remarkably fast at the highest As, overpressure used. Selectivity was, however, more difficult to achieve in these conditions and a high As-4 pressure was shown to be able to suppress reevaporation of the polycrystalline deposits on the mask.