Since Stormer and Tsang have introduced the two-dimensional hole gas (2DHG) in the GaAs/AlGaAs heterosystem, the choice of suitable dopants was limited to beryllium and silicon over the last 20 years. Both acceptor atoms have significant disadvantages, i.e., either high diffusion rates or a limitation to specific growth directions. Utilizing a carbon filament doping source we prepared high-quality 2DHGs in the (001) and the nonpolar (110) crystal plane with carrier mobilies beyond 106 cm2/V s in quantum-well and single-interface structures. Low temperature magnetoresistance measurements recover a large number of fractional quantum Hall effect states and show a pronounced beating pattern from which the Rashba-induced spin splitting has been determined. In addition, 2DHGs have been grown on cleaved edges of (110) and (001) wafers with transport features in qualitative agreement with our findings on (110) substrates.