Left: Redshift evolution of the cold gas metallicity as a function of stellar mass (following Fontanot et al. 2021, we apply a downwards 0.1 dex shift to the intrinsic predictions). Right: Stellar mass-metallicity relation at different redshifts. The line types and colours are as in Fig. A.1. In both panels the data points correspond to the compilation used in Fontanot et al. (2021, see complete reference list for their Fig. 1).