Not yet reviewed by Pith; the record is open.

We investigate the distribution and evolution of HI gas in different theoretical models, including hydro-dynamical simulations (Illustris-TNG and SIMBA), semi-analytic models (GAEA), and the empirical models ( NeutralUniverseMachine; NUM). By comparing model predictions for the HI mass function (HIMF), HI-halo and HI-stellar mass relations, conditional HI mass function (CHIMF) and the halo occupation distribution (HOD) of HI-selected galaxies, we find that all models show reasonable agreement with the observed HIMF at $z\sim0$, but 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 lower amplitudes of HIMF at the high-mass end. Comparisons of CHIMF distributions indicate that the HIMF is dominated by halos of $10< \log(M_{\rm vir}/M_\odot) <11$ and $11< \log(M_{\rm vir}/M_\odot)<12$ at the low- and high-mass ends, respectively. From the HI HODs of central galaxies, we find that TNG100 overpredicts the number of central galaxies with high $M_{\rm HI}$ in massive halos and GAEA shows a very strong depletion of HI gas in quenched centrals of massive halos. The main cause of the differences is the AGN feedback mechanisms implemented in different models.