We present an analysis of the magnetosphere–ionosphere coupling current system which is associated with the maintenance of plasma corotation in Jupiter's middle magnetosphere. The formulation follows Cowley and Bunce (Planet. Space Sci. 49 (2001) 1067), but here the angular velocity of the equatorial plasma is computed using the steady-state theory of Hill (J. Geophys. Res. 84 (1979) 6554) and Pontius (J. Geophys. Res. 102 (1997) 7137) rather than being determined by a simple empirical model. Results are compared both for a realistic magnetospheric current sheet magnetic field model and for a simple dipole field. The results for the current sheet model confirm previous conclusions concerning current and auroral precipitation distributions based on the empirical angular velocity model. Specifically, we find that upward field-aligned currents flow from the ionosphere to the equatorial current sheet over the whole radial range from ∼20 R J to the outer boundary of the region considered at 100 R J, thus returning from the current sheet to the ionosphere at larger radial distances outside this region. The upward currents are of sufficient intensity to require the existence of field-aligned voltages which accelerate magnetospheric electrons down into the atmosphere, thus creating intense auroras. At ionospheric heights, the upward field-aligned current densities are several tenths of a μA m −2 , flowing in a narrow latitudinal band less than ∼1° wide, located at ∼16° dipole co-latitude. The associated field-aligned voltages are several tens of kV, resulting in precipitated electron energy fluxes capable of exciting UV auroras of hundreds of kR intensity. The model thus forms an appropriate basis on which to understand the origin of Jupiter's ‘main auroral oval’ emissions. For the dipole field, the steady-state equatorial angular velocity profile is found to be very similar to that for the current sheet model. Nevertheless, the different mapping of the field lines to the ionosphere results in a magnetosphere–ionosphere coupling current system which has significantly different properties. In particular, the height-integrated ionospheric Pedersen current intensity is found to be factors of ∼2–3 less than that for the current sheet model, and since the field-aligned current is also found to be spread over a much broader latitudinal band, ∼5° wide centred at ∼10° dipole co-latitude, the field-aligned current density is reduced by more than an order of magnitude. Only small (few kV) field-aligned voltages are thus required to carry the upward current in this case, resulting in much weaker electron precipitation, and much weaker, few kR, UV auroras. Our results thus emphasise that while the magnetic field model may not greatly effect the steady-state angular velocity profile, it nevertheless is of crucial significance in determining the consequent magnetosphere–ionosphere coupling current system, and the resulting auroral precipitation.