In this article, we present an analysis on the transport of charged samples through micro and nanofluidic channels with large zeta potentials (vertical bar zeta vertical bar > (k(B)T)/e). Using the Method of Moments formulation, the diffusion-convection equation has been solved to evaluate the mean velocity and the dispersion of analyte bands in a parallel-plate device under electrokinetically- and pressure-driven flow conditions. The effect of electromigration induced by the lateral electric field within the Debye layer has been quantified in our work using a Peclet number (Pe(t)) based on the characteristic electrophoretic velocity of the solute molecules in the transverse direction. It has been shown that while the effects of transverse electromigration on analyte transport only depends on the product Pe(t)zeta* for vertical bar zeta*vertical bar = (zeta*)/ k(B)T << 1, both these parameters independently affect the flow of charged species in large zeta potential systems. For a given value of Pe(t)zeta*, the mean velocity and the slug dispersivity can vary by as much as an order of magnitude in going from a small zeta potential system (vertical bar zeta*vertical bar << 1) to a channel with vertical bar zeta*vertical bar = 4.