Inviscid equilibrium mean flows over topography are considered for continuously stratified quasi-geostrophic models, in contrast to previous work which has dealt with two-layer models. From the constraint of maximum entropy, an equation for the equilibrium mean flow is derived. Analytical solutions are obtained for uniform and piecewise-constant stratifications. With increasing stratification, the mean streamfunction becomes increasingly bottom intensified. Bottom trapping becomes ever more pronounced on smaller scales, but can remain significant even on the largest scales. When boundary temperature is uniform, transport is shown to be independent of stratification, other factors being equal. Although two-layer models share this property, they represent poorly the energetics of the continuous system when bottom trapping is significant.