We report on the growth and electrical characterization of a series of two-dimensional hole systems (2DHSs) used to study the density dependence of low temperature mobility in 20 nm GaAs/AlGaAs quantum wells. The hole density was controlled by changing the Al mole fraction and the setback of the delta-doping layer. We varied the density over a range from 1.8 × 10 10 cm −2 to 1.9 × 10 11 cm −2 finding a nonmonotonic dependence of mobility on density at T = 0.3 K. Surprisingly, a peak mobility of 2.3 × 10 6 cm 2 /Vs was measured at a density of 6.5 × 10 10 cm −2 with further increase in density resulting in reduced mobility. We discuss possible mechanisms leading to the observed non-monotonic density dependence of the mobility. Relying solely on interface roughness scattering to explain the observed drop in mobility at high density requires roughness parameters which are not consistent with measurements of similar electron structures. This leaves open the possibility of contributions from other scattering mechanisms at high density.Two-dimensional hole systems (2DHSs) on (001) oriented GaAs offer an interesting alternative to the more widely studied two-dimensional electron systems (2DESs). 2DHSs on (001) GaAs have effective masses roughly 4.5 to 7.5 times larger 1-3 than that in corresponding 2DESs which increases the importance of Coulomb interactions relative to the kinetic energy resulting in enhancement of importance of many-body effects. In addition, the p-wave symmetry of the valence band in GaAs leads to a much reduced hyperfine coupling of hole spins to the atomic nuclei which makes them an exciting alternative to electrons for quantum dot spinbased qubits [4][5][6] . The presence of spin-orbit coupling and light/heavy hole mixing in the valence band of GaAs also allows extensive band structure engineering 7-9 . This feature has been exploited to alter the nature of groundstates in the quantum Hall regime.