We present an experimental study of the evolution of the surface of a growing film as a function of the statistical parameters of the virgin substrate roughness. The growth of sputter-deposited Al2O3 films onto Si substrates was followed in situ using an x-ray scattering technique. Despite the use of substrates presenting different roughness correlation length and cristallographie orientation, the evolution of the film roughness is demonstrated to obey the same scaling law, i.e., with the same static and dynamic exponents. Approaches to accurately determine the scaling exponents from x-ray scattering data are discussed. © 2010 IOP Publishing Ltd.