H₂ mass function at z = 0.1, 1.0, and z = 2.0. The error bars represent Poissonian errors for each stellar mass bin, typically smaller than the size of the point. The shaded green region encompasses the full dispersion of the individual H₂MFs corresponding to each of the five simulation boxes. In the local Universe, we report for comparison the H₂ mass function obtained by Andreani et al. (2020), who use a fixed (COfix) or a luminosity dependent (CO-L) CO-to-H₂ conversion factor and the best-fit model of Rodríguez-Puebla et al. (2020) and Fletcher et al. (2021). At higher redshifts, the boxes show constraints from Decarli et al. (2016) (ALMA ASPECS-Pilot survey), Decarli et al. (2019) (ALMA ASPECS-LP survey), and Riechers et al. (2019) (COLDz survey). The H2MF at redshift z = 0 is also shown in the middle and right panels using a thin dotted line to facilitate comparison.