This paper presents for the simple flow over a flat plate the near-wall profiles of mean flow and turbulence quantities determined with seven eddy-viscosity turbulence models: the one-equation turbulence models of Menter and Spalart & Allmaras; the k−w two-equation model proposed by Wilcox and its TNT, BSL and SST variants and the k−√kL two-equation model. The results are obtained at several Reynolds numbers ranging from 107 to 2.5×109. Sets of nine geometrically similar Cartesian grids are adopted to demonstrate that the numerical uncertainty of the finest grid predictions is negligible. The profiles obtained numerically have relevance for the application of so-called ‘wall function’ boundary conditions. Such wall functions refer to assumptions about the flow in the viscous sublayer and the ‘log law’ region. It turns out that these assumptions are not always satisfied by our results, which are obtained by computing the flow with full near-wall resolution. In particular, the solution in the ‘log-law’ region is dependent on the turbulence model and on the Reynolds number, which is a disconcerting result for those who apply wall functions.