We introduce high mobility two-dimensional hole systems (2DHSs) in AlGaAs/GaAs heterosystems grown by molecular beam epitaxy (MBE). Utilizing a carbon filament source, two-dimensional hole gases (2DHGs) were fabricated on the (0 0 1) and (1 1 0) crystal plan. These samples exhibit low-temperature mobilities beyond 106 cm2/V s at densities varying from 0.6 to 2.3×1011 cm−2. In order to explore the subband structure as a function of carrier density, aluminum top gates were deposited on the samples. The carrier density was found to show a hysteretic behavior when tuned with an external electric field. The origin of this effect will be discussed. It opens a way to adjust the hole density in a wide range within a single sample in the absence of an externally applied electric field.