Abstract Monolayers of hexagonal boron nitride (hBN) are grown on graphite substrates using high-temperature molecular beam epitaxy (HT-MBE). The hBN monolayers are observed to grow predominantly from step edges on the graphite surface and exhibit a strong dependence of the morphology, including the dominant crystallographic edge, of the hBN monolayers, on the growth temperature, as well as systematic variations in growth rate and coverage, and significant differences in the growth at monolayer and multilayer graphite steps. At graphite monolayer steps hBN grows laterally across the surface on the lower terrace, but hBN growth on the upper side of the graphite step is more limited and is nucleated by three-dimensional clusters. Multilayer graphite steps exhibit a much higher density of non-planar hBN aggregates and growth on both the upper and lower terraces occurs. The results show that the hBN monolayer growth edge type, hBN island shape and the presence of hBN aggregates can be controlled in HT-MBE, with the highest quality layers grown at a substrate temperature of about 1390 °C. Sequential HT-MBE growth of hBN, graphene (G) and a second cycle of hBN growth results in the formation of monolayer thick lateral hBN–G–hBN heterostructures, in which a strip of G is embedded between monolayers of hBN.