We present a study of transport in graphene devices on polar insulating substrates by solving the Boltzmann transport equation in the presence of graphene phonon, surface polar phonon, and Coulomb charged impurity scattering. The value of the saturated velocity shows very weak dependence on the carrier density, the nature of the insulating substrate, and the low-field mobility, varied by the charged impurity concentration. The saturated velocity of 4× 107 -8× 107 cm/s calculated at room temperature is significantly larger than reported experimental values. The discrepancy is due to the self-heating effect which lowers substantially the value of the saturated velocity. We predict that by reducing the insulator oxide thickness, which limits the thermal conductance, the saturated currents can be significantly enhanced. We also calculate the surface polar phonon contribution to the low-field mobility as a function of carrier density, temperature, and distance from the substrate. © 2010 The American Physical Society.