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Abstract Intensive research has been carried out on two-dimensional materials, in particular molybdenum disulfide, towards high-performance field effect transistors for integrated circuits1. Fabricating transistors with ohmic contacts is a challenging task due to the formation of a high Schottky barrier that severely limits the performance of the transistors for real-world applications. Graphene-based heterostructures can be used in addition to, or as a substitute for unsuitable metals. In this paper, we present lateral heterostructure transistors made of scalable chemical vapor-deposited molybdenum disulfide and chemical vapor-deposited graphene achieving a low contact resistances of about 9 kΩ·µm and high on/off current ratios of 108. Furthermore, we also present a theoretical model calibrated on our experiments showing further potential for scaling transistors and contact areas into the few nanometers range and the possibility of a substantial performance enhancement by means of layer optimizations that would make transistors promising for use in future logic integrated circuits.