N

We investigate the distribution and evolution of H <ns0:sc>I</ns0:sc> gas in different theoretical models, including hydrodynamical simulations of IllustrisTNG and SIMBA, the semi-analytical model of GAEA, and the empirical model of N<ns0:sc>EUTRAL</ns0:sc>U<ns0:sc>NIVERSE</ns0:sc>M<ns0:sc>ACHINE</ns0:sc> (NUM). By comparing model predictions for the H <ns0:sc>I</ns0:sc> mass function (HIMF), H <ns0:sc>I</ns0:sc>-halo and H <ns0:sc>I</ns0:sc>-stellar mass relations, conditional H <ns0:sc>I</ns0:sc> mass function (CHIMF) and the halo occupation distribution (HOD) of H <ns0:sc>I</ns0:sc>-selected galaxies, we find that all models show reasonable agreement with the observed HIMF at z ∼ 0. However, the differences become much larger at higher redshifts of z = 1 and z = 2. The HIMF of NUM shows remarkable agreement with the observation at z = 1, whereas other models predict much smaller amplitudes of HIMF at the high-mass end. Comparisons of CHIMF distributions indicate that the HIMF is dominated by haloes of 10 < log(Mvir/M⊙) < 11 and 11 < log(Mvir/M⊙) < 12 at the low- and high-mass ends, respectively. From the H <ns0:sc>I</ns0:sc> HODs of central galaxies, we find that TNG100 overpredicts the number of central galaxies with high MH <ns0:sc>I</ns0:sc> in massive haloes, and that GAEA shows a very strong depletion of H <ns0:sc>I</ns0:sc> gas in quenched centrals of massive haloes. The main cause of these differences is the AGN feedback mechanisms implemented in different models.