The electrical properties of InN nanowires were investigated in four-point probe measurements. The dependence of the conductance on the wire diameter allows distinguishing between "core" bulk (quadratic) and "shell" sheet (linear) contributions. Evidence of the formation of a thin In(2)O(3) layer at the surface of the nanowires is provided by X-ray core level photoemission spectroscopy. The shell conductivity is therefore ascribed to an electron accumulation layer forming at the radial InN/In(2)O(3) interface. Although conductance through the accumulation layer dominates for nanowires below a critical diameter of about 55 nm, the core channel cannot be neglected, even for small nanowires.