The authors demonstrate the heteroepitaxial and homoepitaxial growth of single crystalline beta-Ga2O3 by plasma-assisted molecular beam epitaxy. Phase-pure ((2) over bar 01) and (100) beta-Ga2O3 thin films were grown on c-plane sapphire and (100) beta-Ga2O3 substrates, respectively. Based on the homoepitaxial results, detailed information is reported on the dependence between the beta-Ga2O3 film quality and various growth parameters. At an optimized growth temperature of 700 degrees C, a growth relationship between growth rates and increasing gallium fluxes was established at a fixed oxygen pressure. A three-dimensional columnar growth with a relatively high growth rate was measured at a low gallium flux while a terrace surface morphology with a reduced growth rate was observed as the gallium flux increased. The gallium flux played an important role on both surface morphology and growth rate. We associated the decreasing growth rate with increasing gallium flux with the formation of gallium suboxides monitored by quadrupole mass spectrometry. The formation and desorption of volatile gallium suboxides limited the resulting growth rate of beta-Ga2O3 growth. (C) 2010 American Vacuum Society. [DOI: 10.1116/1.3294715]