Same as Fig. 3, but with coloured lines representing different metallicity bins for the BH host galaxy. At z < 10 observable BHs are preferentially hosted by galaxies with Log(Z/Z_⊙) ≥ −2, whereas at higher redshifts an increasing fraction of observable systems resides in galaxies with −3 ≤ Log(Z/Z_⊙) < −2.