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GaN/AlxGa1-xN heterostructures were grown by metal-organic vapor phase epitaxy (MOVPE) to study in detail the formation of two-dimensional hole gases (2DHG). In contrast to the common double-heterostructure approach to create 2DHG, which is based on GaN buffer layers and leads to the parallel formation of a two-dimensional electron gas (2DEG), this concept is designed to create a 2DHG only. The Al mole fraction in the AlGaN buffer and the GaN channel thickness are each varied to investigate their influence on 2DHG properties. The carrier concentrations as determined by room temperature Hall measurements follow the expected trend given by the Al content dependence of the spontaneous polarization of the relaxed AlGaN buffer. A 2DHG density as high as of 1.6·1013 cm-2 with a negligible dependence on temperature (80 – 300 K) is determined for a GaN/Al0.29Ga0.71N heterostructure by temperature-dependent Hall measurements. Higher carrier concentrations can also be achieved, yet strain relaxation of the GaN channel degrades the transport properties for Al contents above 30 %.