The total transport of Antarctic Bottom Water across the Rio Grande Rise, including the western boundary, the Vema Channel, and the Hunter Channel is estimated from hydrographic measurements across these pathways. The contribution of the Vema Channel is greatest at 3.9 X 10(6) m(3) s(-1), which is very close to earlier estimates. The western boundary current contribution is 2.0 X 10(6) m(3) s(-1) and that of the Hunter Channel 0.7 X 10(6) m(3) s(-1). The lower values outside the Vema Channel are offset by the important source of mass they form to the lower density classes of bottom water. About 40% of the now is concentrated in the highest density class representing the source of Weddell Sea Deep Water to the Brazil Basin. The flow structure is characterized by horizontal and vertical recirculation.