Growth of GaN by rf-plasma molecular beam epitaxy leads to different surface morphologies for nitrogen-stable growth versus gallium-stable growth. Nitrogen-stable growth produces a granular surface morphology with many samples having a significant density of pyramidal hillocks. In contrast, gallium-stable growth results in a flat surface morphology. The hillocks were directly linked to the presence of inversion domains which originated in the nucleation layer. Nitrogen-stable growth and growth under atomic hydrogen enhanced the growth rate of inversion domains with respect to the surrounding matrix, while growth under Ga-stable conditions resulted in a more nearly equal growth rate. Evidence is presented suggesting that hydrogen may stabilize the surface of growing GaN.