  We extend the local stellar galaxy-(sub)halo connection to the atomic
hydrogen (HI) component by seeding semi-empirically galaxies into a large
N-body dark matter (DM) simulation. The main input to construct the mock galaxy
catalogue are: our constrained stellar mass-to-(sub)halo circular velocity
($M_{\ast}$-$V_{\rm DM}$) relation, assuming a scatter independent of any
galaxy property, and the empirical $M_{\rm HI}$ conditional probability
distributions given $M_{\ast}$ for central and satellite galaxies. We find that
the $\langle\log M_{\rm HI}\rangle-\log M_{\rm DM}$ relation is not a monotonic
increasing function. It increases with mass up to $M_{\rm DM}\sim 10^{12}$
$M_{\odot}$, attaining a maximum of $\langle\log(M_{\rm HI}/M_{\odot})\rangle
\sim 9.2$, and at higher (sub)halo masses, $\langle\log(M_{\rm HI})\rangle$
decreases slightly with $M_{\rm DM}$. The scatter around it is also large and
mass dependent. The bivariate $M_{\rm HI}$ and $M_{\rm DM}$ distribution is
broad and bimodal, specially at $M_{\rm DM}\gtrsim 10^{12}$ $M_\odot$, which is
inherited from the input $M_{\rm HI}$ conditional distributions. We also report
the total (central+satellites) HI gas mass within halos, $\langle M^{\rm
tot}_{\rm HI}(M_{\rm DM})\rangle$, as a function of $M_{\rm DM}$. The mean
$M^{\rm tot}_{\rm HI}-M_{\rm DM}$ relation is an increasing monotonic function.
The galaxy spatial clustering increases weakly as the $M_{\rm HI}$ threshold
increases. Our HI mock galaxies cluster more in comparison to the blind HI
ALFALFA (Arecibo Fast Legacy ALFA) survey but we show that it is mainly due to
the selection effects. We discuss the implications of our results in the light
of predictions from semi-analytical models and hydrodynamics simulations of
galaxy evolution.
