Impact of our main prescriptions for regulating star formation and gas accretion, photoionisation, re-accretion, and thermal instabilities on the stellar mass assembly of model galaxies (i.e. the co-moving density of model galaxies as a function of redshift). The solid red line shows our fiducial model using the full suite of prescriptions. The dot-dashed gold lines indicate our model without photoionisation. In the three right-most panels, the dotted brown lines and dashed orange lines indicate predictions of the stellar mass functions without including the prescriptions for re-accretion of gas over two halo crossing times and thermal instabilities, respectively (as indicated in the legends of the two left-most panels). These are compared to the observational estimates of the co-moving density of galaxies from Davidzon et al. (2016). The four different panels represent four different redshift bins, z = 0.3, 1.5, 2.8, and 4 (from the left-most to the right-most panel, respectively).