This paper reports a full two-dimensional numerical computation of the particle distributions, electric fields, and currents associated with a standard adiabatic model of a quiet auroral arc and inverted-V potential. Both the region of auroral electron precipitation and the return current region are modeled; for the latter we assume a normal return current dominated by ambipolar E∥, with no substantial downward E∥. We go beyond earlier treatments of the adiabatic model (which either had no coupling between different field lines or treated all field lines as having essentially identical conditions along B) by specifying latitudinal variations in particle sources and parallel potential drops, which require every field line to be treated separately, coupled to other lines by current conservation. In particular, differential pitch angle anisotropies which drive upward E∥ are varied with latitude in order to accommodate a smooth transition to the return current region. In this transition regime the model predicts density enhancements on field lines at the edge of the inverted V that have only a small potential drop. We believe this is the first work to address the return current region with a realistic adiabatic model of the magnetosphere, including particle populations of both magnetospheric and ionospheric origin.