Similar to Fig. 5 but showing the final masses of stars as a function of the CO core mass M_CO at core collapse. In all three panels, single-star models are plotted as blue squares. We further indicate models that experience SN fallback by grey squares while crosses mark those models that should have experienced enhanced LBV-like mass loss, which is not accounted for in our models (see Sect. 2.1). The dotted black line is a one-to-one relation.