  We quantitatively investigate the dependence of central galaxy HI mass
($M_{\rm HI}$) on the stellar mass ($M_\ast$), halo mass ($M_{\rm h}$), star
formation rate (SFR), and central stellar surface density within 1 kpc
($\Sigma_1$), taking advantage of the HI spectra stacking technique using both
the Arecibo Fast Legacy ALFA Survey and the Sloan Digital Sky Survey. We find
that the shapes of $M_{\rm HI}$-$M_{\rm h}$ and $M_{\rm HI}$-$M_\ast$ relations
are remarkably similar for both star-forming and quenched galaxies, with
massive quenched galaxies having constantly lower HI masses of around 0.6 dex.
This similarity strongly suggests that neither halo mass nor stellar mass is
the direct cause of quenching, but rather the depletion of HI reservoir. While
the HI reservoir for low-mass galaxies of $M_\ast<10^{10.5}M_\odot$ strongly
increases with $M_{\rm h}$, more massive galaxies show no significant
dependence of $M_{\rm HI}$ on $M_{\rm h}$, indicating the effect of halo to
determine the smooth cold gas accretion. We find that the star formation and
quenching of central galaxies are directly regulated by the available HI
reservoir, with an average relation of ${\rm SFR}\propto M_{\rm
HI}^{2.75}/M_\ast^{0.40}$, implying a quasi-steady state of star formation. We
further confirm that galaxies are depleted of their HI reservoir once they drop
off the star-formation main sequence and there is a very tight and consistent
correlation between $M_{\rm HI}$ and $\Sigma_1$ in this phase, with $M_{\rm
HI}\propto\Sigma_1^{-2}$. This result is in consistent with the
compaction-triggered quenching scenario, with galaxies going through three
evolutionary phases of cold gas accretion, compaction and post-compaction, and
quenching.
