This article develops the theoretical analysis of transport and dispersion phenomena in wide-bore chromatography at values of the Peclet number Pe beyond the upper bound of validity of the Taylor-Aris theory. It is shown that for Poiseuille flows in cylindrical capillaries the average residence time grows logarithmically with the Peclet number, while the variance of the outlet chromatogram scales as the power 1/3 of Pe. In the presence of slip boundary conditions, both the mean and the variance of the outlet chromatograms saturate at high Pe, and this phenomenon provides an indirect transport-based way to detect slip flow conditions at the solid walls and, more generally, flow distributions in channel flows.