Formation !efficiency (i.e. number of systems formed per unit of star-forming mass, ) of different types of CBM at different metallicities. We compute a grid of 32 different metallicities (indicated with filled squares at the BH–BH curves), ranging from 0.005 Z_⊙ to 1.5 Z_⊙. We indicate three different models: M10 in blue (initial distributions of Sana et al. 2012), I1 in green (initial distributions of MD17) and I2 in red (same as I1 but with a top-heavy IMF at low metallicities; see Eq. (2)). We note that model I2 is only different from I1 at Z < 0.004 = 0.2 Z_⊙.