Vapor transport growth of atomically thin MoS₂ layers on patterned substrates is investigated, as it is a step towards the self-aligned growth and formation of heterojunctions, which could be useful in future applications. Enhanced formation of MoS₂ flakes at the pattern edges is observed on both the substrates examined, namely, patterned thermal SiO₂ on Si(100) and graphene flakes on SiO₂. The diffusion driven growth leads to the formation of MoS₂ monolayers (MLs) with sizes of tens of micrometers around the edges of SiO₂ patterns. The growth mode and the optical quality of the MoS₂ flakes can be controlled by varying the substrate temperature. Besides the lateral growth, 3R-type pyramids are obtained on prolonging the growth. Lateral MoS₂-graphene heterostructures are obtained by using graphene flakes on SiO₂ as a substrate.