Nominally-undoped Ga2O3 layers were deposited on a-, c- and r-plane sapphire substrates using pulsed laser deposition. Conventional x-ray diffraction analysis for films grown on a- and c-plane sapphire showed the layers to be in the β-Ga2O3 phase with preferential orientation of the (-201) axis along the growth direction. Pole figures revealed the film grown on r-plane sapphire to also be in theβ-Ga2O3 phase but with epitaxial offsets of 29.5°, 38.5° and 64° from the growth direction for the (-201) axis. Optical transmission spectroscopy indicated that the bandgap was ~5.2eV, for all the layers and that the transparency was > 80% in the visible wavelength range. Four point collinear resistivity and Van der Pauw based Hall measurements revealed the β-Ga2O3 layer on r-plane sapphire to be 4 orders of magnitude more conducting than layers grown on a- and c-plane sapphire under similar conditions. The absolute values of conductivity, carrier mobility and carrier concentration for the β-Ga2O3 layer on r-sapphire (at 20Ω-1.cm-1, 6 cm2/Vs and 1.7 x 1019 cm-3, respectively) all exceeded values found in the literature for nominally-undoped β-Ga2O3 thin films by at least an order of magnitude. Gas discharge optical emission spectroscopy compositional depth profiling for common shallow donor impurities (Cl, F, Si and Sn) did not indicate any discernable increase in their concentrations compared to background levels in the sapphire substrate. It is proposed that the fundamentally anisotropic conductivity in β-Ga2O3 combined with the epitaxial offset of the (-201) axis observed for the layer grown on r-plane sapphire may explain the much larger carrier concentration, electrical conductivity and mobility compared with layers having the (-201) axis aligned along the growth direction.