The grain size evolution of polycrystalline thin films, which form by competitive grain overgrowth as commonly interpreted using the van der Drift model, is understood to follow a power-law scaling of the average grain size d with film thickness h, i.e. d proportional to h(proportional to). While simulations have identified a growth exponent alpha = 0.4 for three-dimensional growth, previous experimental studies did not confirm this value, instead finding alpha values in the range of similar to 0.5-0.7. Here we study competitive grain overgrowth using a system of ZnO thin films grown by low-pressure metal-organic chemical vapor deposition. We present quantitative data on the evolution of grain size and orientation across the thickness of thin films, obtained by automated crystal orientation mapping of 'double-wedge' transmission electron microscopy samples. The data from alpha-textured ZnO films, grown under three different conditions, are compared against van der Drift model predictions of self-similarity of the grain size distribution and the power-law scaling. The results are further interpreted by comparing to simulations of faceted polycrystalline film growth, which we adapt to the ZnO system by including idiomorphic growth shapes with a six-fold symmetry and random or biased nuclei orientations. As well as showing the predicted self similarity of grain size distributions during growth, for the first time our experimental data confirm a power-law growth exponent of alpha = 0.4, as also predicted by the simulations using randomly oriented nuclei. Nevertheless, interpretation of this result is contingent on the absence of factors such as textured nucleation and renucleation during film growth. Indeed, only one film, grown at a higher ratio of H2O/ DEZ precursor gases, displaying random initial nucleation, and minimal grain renucleation during growth, shows a proper conformance to the model nature and predictions. (C) 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.