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 $langlelog M_{rm HI}rangle-log M_{rm DM}$ 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 $langlelog(M_{rm HI}/M_{odot})rangle sim 9.2$, and at higher (sub)halo masses, $langlelog(M_{rm HI})rangle$ 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.
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