[en] Based on an ultra-high vacuum compatible two-step molecular beam epitaxy synthesis with elemental sulphur, we grow clean, well-oriented, and almost defect-free monolayer islands and layers of the transition metal disulphides MoS₂, TaS₂ and WS₂. Using scanning tunneling microscopy and low energy electron diffraction we investigate systematically how to optimise the growth process, and provide insight into the growth and annealing mechanisms. A large band gap of 2.55 eV and the ability to move flakes with the scanning tunneling microscope tip both document the weak interaction of MoS₂ with its substrate consisting of graphene grown on Ir(1 1 1). As the method works for the synthesis of a variety of transition metal disulphides on different substrates, we speculate that it could be of great use for providing hitherto unattainable high quality monolayers of transition metal disulphides for fundamental spectroscopic investigations. (paper)