In ultra-thin two-dimensional (2-D) materials, the formation of ohmic contacts with top metallic layers is a challenging task that involves different processes than in bulk-like structures. Besides the Schottky barrier height, the transfer length of electrons between metals and 2-D monolayers is a highly relevant parameter. For MoS2, both short (≤30 nm) and long (≥0.5 μm) values have been reported, corresponding to either an abrupt carrier injection at the contact edge or a more gradual transfer of electrons over a large contact area. Here we use ab initio quantum transport simulations to demonstrate that the presence of an oxide layer between a metallic contact and a MoS2 monolayer, for example TiO2 in case of titanium electrodes, favors an area-dependent process with a long transfer length, while a perfectly clean metal-semiconductor interface would lead to an edge process. These findings reconcile several theories that have been postulated about the physics of metal/MoS2 interfaces and provide a framework to design future devices with lower contact resistances.