We have exploited conductive atomic force microscopy (CAFM) to characterize the vertical current transport from graphene (Gr) to the 2D electron gas of AlxGa1 xN/GaN heterostructures considering different kinds of AlGaN surfaces in terms of roughness and unevenness. The vertical current transport mechanism can radically change depending on these nanometer size superficial fluctuations whereby the nanoscale lateral resolution of CAFM current voltage (IV) measurements offers the ideal conditions to distinguish this effect form the average macroscopic behavior. We have characterized bare and Gr coated high quality AlGaN surface at first, observing for both a rectifying behavior. In particular the contact on Gr shows a lower Schottky barrier height (SBH)(ΦB= 0.4 eV) than the bare AlGaN (ΦB= 0.9 eV), and a smaller spread between the array of sampled positions. In particular this lateral homogeneity can be …