If discrete arcs and inverted V's are associated with current sheets and the U shaped electric potential structure, then existing two-dimensional models are probably inadequate. The rapid east-west electric-field associated flow in the arms of the U shaped potential structure requires that there must be a substantial inflow to the outflow from each arm somewhere along the system since arcs and inverted V's have a limited east-west extent. Thus strong north-south polarization currents occur as the plasma enters and leaves the arms of the U. It is hypothesized that these currents, determine the north-south thickness. Three representative three-dimensional models are considered in which the current sheets are either tangential or rotational discontinuities modified by the U shaped potential structure. Thicknesses of the order of a few tens of kilometers are obtained. The occurence and type of discontinuity expected at various locations in the magnetosphere are considered. Discontinuities and hence inverted V's and/or arcs are expected at the interface between open and closed field lines, which explains quiet time polar cap sun-aligned arcs, and at interfaces between plasmas which have merged or been injected on the dayside or reconnected on the nightside in different impulsive events. The last two account for arcs occurring near the throat at active times and for parallel arcs within the oval. The occurrence of long parallel arcs within the oval is encouraged by the convective flow pattern and by the differences in precipitation from flux tubes with differential histories.