The Stommel and Arons <1960a, b> theory of the deep circulation of the world ocean does not directly address the physics of deep boundary currents. In the present paper a maximally simple steady state physics for deep western boundary currents is developed and integrated into the Stommel-Arons model. This is accomplished by modifying the assumptions of the latter to include effective horizontal eddy viscous terms everywhere in the deep water, including in the interior. The resulting solution for the meridional velocity in a rectangular ocean on a beta plane is mathematically analogous to that of Munk <1950> for the wind-driven circulation. In the interior the meridional velocity reduces identically to that of Stommel and Arons. Among other benefits, the solution eliminates the theoretical difficulties associated with the crossing of the equator by the deep western boundary current. As an initial test of the theory's consistency with observation, theoretical plots of pressure and meridional velocity as a function of longitude are qualitatively compared with hydrographic sections and inferred meridional velocity fields in the eastern and western basins of the abyssal North Atlantic. Also, the theoretical profile for the meridional velocity as a function of longitude is qualitatively compared with observations of longshore velocity as a function of offshore distance in the deep western boundary current of the North Atlantic Deep Water. ¿ 1998 American Geophysical Union