In this paper, we show that Graphene (Gr) can provide highly laterally homogeneous Schottky or ohmic contacts to AlxGa1-xN/GaN heterostructures even without any thermal treatment. Current transport from Gr to the AlGaN/GaN Two Dimensional Electron Gas (2DEG) was investigated by local I-V measurements using Conductive Atomic Force Microscopy (CAFM). The AlGaN microstructure was found to play a key role on the transport properties at Gr/AlGaN interface. Gr contacts onto a uniform and defect-free AlGaN barrier layer exhibits a rectifying behaviour with a lower and much more uniform Schottky barrier with respect to common metals. Interestingly, a highly uniform ohmic contact is obtained with Gr on AlGaN layers with a properly chosen microstructure, i.e in the presence of a large density of V-shaped defects which locally reduce the AlGaN thickness. Noteworthy, the ohmic behaviour on AlGaN/GaN …