Different equilibria of oceanic thermohaline circulation may exist under the same forcing conditions. One of the reasons for the existence of these multiple equilibria is a feedback between the overturning circulation and the advective transport of salt and heat. In an equatorially symmetric configuration, the multiple equilibria arise through symmetry-breaking pitchfork bifurcations when the strength of the freshwater forcing is increased. Here, continuation methods are used to track the fate of the different equilibria under equatorially asymmetric conditions in a three-dimensional, low-resolution ocean general circulation model in an Atlantic-like basin coupled to an energy-balance atmosphere model. The effect of the continental geometry, the presence of the Antarctic Cir- cumpolar Current (ACC), and asymmetric air-sea interaction on the preference of equilibria are considered. Although all asymmetry-inducing mechanisms favor northern Atlantic sinking states, the open Southern Ocean and ACC are shown to be substantial contributors. The origin of the hysteresis behavior between strong and weak overturning states is clarified in terms of the overall bifurcation picture. The disappearance of a class of southern sinking equilibria because of the combined effects of all asymmetry mechanisms leads to a substantial regime with a unique steady state. The relationship between the hysteresis regime and the unique-state regime provides a larger context for quantitative determination of the relevance of each to climate.