An undoped AlGaN/GaN nanowire demonstrated p-type conductivity based solely on the formation of hole carriers in response to the negative polarization field at the (000-1) AlGaN/GaN facet. A transistor based on this nanowire displayed a low-voltage transition from Ohmic to space charge limited conduction. A numerical simulation showed that a highly asymmetric strain exists across the triangular cross-section, which creates a doublet peak in the piezoelectric induced polarization sheet charge at the (000-1) facet. Additionally, there is a strong interplay between the charge at the (000-1) AlGaN/GaN interface with depletion from the three surfaces as well as an interaction with the opposing polarization fields at two semi-polar {-110-1} facets. The charge distribution and resultant conduction regime is highly interdependent on configuration of the multi-layer structure, and is not amenable to an analytical model.