Modulation-doped (Al,Ga)As two-dimensional hole gas (2DHG) structures have been grown by molecular-beam epitaxy (MBE) on the (311)A surface of GaAs using silicon as a p-type dopant. Systematic variations of carrier density p(s) and mobility mu with undoped spacer thickness were observed at 1.7 K, with a peak mobility of 4.95 X 10(5) CM2 V-1 s-1 at a sheet carrier density of 2.2X10(11) cm-2 occurring at a spacer thickness of 200 angstrom. The mobility and carrier density of all samples were also measured over the temperature range 300 mK to 4.2 K. These results lead to the conclusion that for samples with spacer thicknesses greater than 400 angstrom, acoustic phonon scattering limits the mobility at low temperatures, whereas for samples with spacer thicknesses less than this value, ionized impurity scattering was observed to be the dominant scattering mechanism. As observed with electron gases, an increase in mobility was achieved by using a thicker region of lightly doped (Al,Ga)As, giving a sample with a mobility of 7.2 X 10(5) CM2 V-1 s-1, at a carrier density of 8.7 x 10(10) cm-2 measured at 300 mK. This value constitutes the highest mobility so far reported, at carrier densities below 1 X 10(11) cm-2.