Heavily doped epitaxial ZnO:Al and Zn1-xMgxO:Al films were grown by radio frequency magnetron sputtering onto single crystalline substrates (sapphire, MgO, silicon) and characterized by structural and electrical measurements. It is the aim of this investigation to better understand the carrier transport and the doping mechanisms in heavily doped transparent conducting oxide (TCO) films. It was found that the crystallographic film quality determines only partly the mobilities and the carrier concentrations: ZnO:Al films on a-plane (110) sapphire and on MgO (100) exhibit the highest mobilities. The oxygen partial pressure during the deposition from ceramic targets is more important influencing especially the carrier concentration N of the films. Though the films grew epitaxially grain boundaries are still existent, which reduce the mobility due to electrical grain boundary barriers for N < 3 (.) 10(20) cm(-3). From annealing experiments the role of point defects and dislocations for the carrier transport could be estimated. For carrier concentrations above 3 (.) 10(20) cm(-3) ionized impurity scattering limits the mobility, which is in agreement with our earlier review [K. Ellmer, J. Phys. D: Appl. Phys. 34 (2001) 3097]. (c) 2005 Elsevier B.V. All rights reserved.