The meridional transport of mass and heat in the South Atlantic as well as the interocean exchange with the South Pacific and Indian Ocean is examined using a model based on the adjoint method. Large amounts of historical temperature (θ) and salinity (s) data are assimilated and an optimal model circulation is searched to satisfy two main objectives: (1) the vertical shear of the model flows is consistent with geostrophic shear estimates, and (2) the model flows correctly reproduce the measured distributions of θ and s. Information on baroclinic flows contained in the historical θ/s distributions is incorporated in the model circulation via constraint 1, and the unknown reference velocities are chosen in a way such that the resulting absolute flow velocities (horizontal and vertical) yield realistic θ and s fields (constraint 2). The model is mass, heat, and salt conserving and has realistic topography. It is shown that realistic θ and s model distributions can be obtained with flows that are consistent with geostrophy. The model-derived reference velocities (2500 dbar) show southward flow of North Atlantic Deep Water (NADW) along the South American coast and show eastward flow along the path of the Antarctic Circumpolar Current (ACC). Satisfactory θ/s simulations are obtained for a variety of model flows that differ considerably with respect to strength of the meridional overturning cell, magnitude of meridional heat transport and inflow rate of Indian Ocean Central (thermocline) Water (IOCW) into the South Atlantic. A strong correlation is found between meridional heat transport, strength of the meridional cell and inflow from the Indian Ocean. For all the model states that were found to be consistent with hydrographie data, the northward transport above the NADW layer is dominated by intermediate water with only relatively small contributions of warm surface water. The maximal acceptable meridional heat transport across 30°S amounts to 0.35 PW. Inflow (shallow and intermediate) from the Indian Ocean into the South Atlantic in the range of 4–7 Sv can be accommodated by the model, but larger values have to be rejected. All acceptable model solutions show net heat gain of the South Atlantic from the atmosphere and a net export of warm water into the Indian Ocean.