We propose a simple illustrative axisymmetric model of the plasma flow and currents in Jupiter's polar ionosphere which are due both to internal magnetospheric plasma processes and the solar wind interaction. The plasma flow in the model is specified using a combination of observations, previous modeling, and theory, and the ionospheric and field-aligned currents are then calculated. With increasing latitude, the model represents conditions in the inner, middle, and outer magnetosphere on closed field lines and on open field lines mapping to the tail lobes. The model allows us to address three important topics, concerned with the closure of the upward field-aligned currents flowing in the middle magnetosphere region, the energy transfers from planetary rotation to polar upper atmosphere heating and to the magnetosphere, and the relative significance of auroral processes associated with the boundary of open field lines (and hence with the solar wind interaction) and with the middle magnetosphere. It is shown in particular that the energy transfers to the polar upper atmosphere and magnetosphere are of order hundreds of TW each and that discrete auroral precipitation is expected both at the boundary of open field lines and in the middle magnetosphere, though being dominated by the latter. While the initial calculations assume for simplicity a constant ionospheric conductance, we also present a development of the model in which the conductance is self-consistently increased in regions of upward field-aligned current by the precipitation of accelerated electrons. It is shown that this feedback acts to spread the upward current in the region equatorward of the open field line boundary, thus reducing the energy flux and total power of precipitating auroral electrons in this region. At the same time it concentrates the upward current in the equatorward part of the middle magnetosphere, thereby increasing the energy flux and total power of precipitating electrons in this region.