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tokens: it is challenging to reproduce this effect in our simulations without additional feedback. Stars from cold accretion mostly formed at high redshifts in small haloes that later assembled into the massive galaxies. The most efficient way to remove them from our simulations is to have stronger winds, i.e. stronger mass-loading factors in those haloes. However, having too much winds early will unavoidably fail to match observations at higher redshifts. The right-hand panels of Figs 10 and 11 show that cold accretion has nearly stopped after = 2 for these galaxies but hot accretion and wind recycling continue growing rapidly at low redshifts, and is responsible for most of the excess stars formed. After = 2, the stars in massive galaxies that must be prevented from forming come from almost equal parts: hot accretion, hot wind re-accretion, and cold wind re-accretion. Hence, preventing hot gas from cooling and forming stars at these times will eliminate both the hot mode accretion and hot wind re-accretion and will lessen the tension in massive haloes. There are several potential mechanisms, such as AGN and cosmic ray heating, that could reduce the amount of this cooling gas but they are not yet included in our simulations. The hot wind recycling would be harder to affect by extra heating, because the higher metallicity of this gas makes it cool faster. In hydrodynamic simulations, mixing between ejected wind elements and the surrounding gas may have a large impact on the amounts of hot and hot wind accretion. It is, however, unclear whether this type of feedback could prevent the ∼1/3 of stars formed through cold wind re-accretion after = 2 from forming, which is also necessary to match the observations. It is possible that a more accurate treatment of the cloud-CGM interaction would allow a larger fraction of these winds to become hot, alleviating this problem. 6 THE HIGH-RESOLUTION SIMULATION OF THE REFERENCE MODEL In this section, we present key results from the high-resolution RefHres simulation. It adopts the new wind launch algorithm as described in the previous sections using our fiducial set of wind parameters listed in Table 1 . It is also implemented with the numerical improvements to the SPH hydrodynamics introduced by Huang et al. ( 2019 ). We will focus on those predictions that have changed significantly from Huang et al. ( 2019 ) and from our previously published work with our new wind algorithm. 6.1 The stellar content Fig. 14 shows that the GSMFs from our fiducial simulation, shown as black lines in each panel, are mostly consistent with observations at all redshifts from = 0 to 4. The agreement is particularly good at the faint end except for = 0, where our simulation slightly underproduces the number of these low-mass galaxies. At the massive end, our GSMFs agree with observations at = 1 and 4. However, our fiducial simulation produces too many massive galaxies at = 0 and too few massive galaxies at = 2, even after taking account