Our goal is to develop some understanding and intuition regarding abyssal ocean circulations. To do this we investigate highly idealized, source/sink-driven flows computed by a single layer, numerical ocean model forced by a prescribed source or sink. The interior circulation is always found to be very slow and Stommel-Arons like. On the other hand, the intense boundary currents may vary considerably from case to case, depending largely upon the potential vorticity (PV) associated with the source or sink. If the source is imposed by downwelling along a northern boundary, then the associated PV flux is zero, and the resulting steady circulation can induce no net frictional torque. The result is a rather complex pattern of boundary layer flow that includes a strong recirculation along the northern boundary. If the same mass flux is injected as a laminar, horizontal inflow, then the associated PV flux is significant, and must be balanced in steady state by frictional torque. The result is a unidirectional boundary layer flow away from the source. Other experiments elucidate the effect of vortex stretching on topography. For example, a horizontal outflow over shallowing topography induces a net cyclonic frictional torque in the boundary layer circulation of the basin. An understanding of the steady state PV balance thus appears to confer some insight into the form of boundary layer flows in these abyssal circulations.