Remnant BH mass versus the ‘leftover’ mass for the models selected when the fiducial CSFH is used (black lines in Figures 1 and 2). These are the remnant and leftover (ejecta) masses when an CC energy injection of 10⁵¹ erg is assumed (Eldridge & Tout 2004), taking into account the mass gap from PISNe and PPISNe (Farmer et al. 2019; Briel et al. 2023). The histograms show the number events expected per 10⁶ M_⊙ of star formation, as described in Figure 3.