[Abridged] We study the abundance and clustering properties of HI at redshifts $zleqslant5$ using TNG100, a large state-of-the-art magneto-hydrodynamic simulation of a 75 Mpc/h box size. We show that most of the HI lies within dark matter halos and quantify the average HI mass hosted by halos of mass M at redshift z. We find that only halos with circular velocities larger than $simeq$ 30 km/s contain HI. While the density profiles of HI exhibit a large halo-to-halo scatter, the mean profiles are universal across mass and redshift. The HI in low-mass halos is mostly located in the central galaxy, while in massive halos is concentrated in the satellites. We show that the HI and matter density probability distribution functions differ significantly. Our results point out that for small halos the HI bulk velocity goes in the same direction and has the same magnitude as the halo peculiar velocity, while in large halos differences show up. We find that halo HI velocity dispersion follows a power-law with halo mass. We find a complicated HI bias, with HI becoming non-linear already at $k=0.3$ h/Mpc at $zgtrsim3$. Our simulation reproduces the DLAs bias value from observations. We find that the clustering of HI can be accurately reproduced by perturbative methods. We identify a new secondary bias, by showing that the clustering of halos depends not only on mass but also on HI content. We compute the amplitude of the HI shot-noise and find that it is small at all redshifts. We study the clustering of HI in redshift-space, and show that linear theory can explain the ratio between the monopoles in redshift- and real-space down to small scales at high redshift. We find that the amplitude of the Fingers-of-God effect is larger for HI than for matter. We point out that accurate 21 cm maps can be created from N-body or approximate simulations rather than full hydrodynamic simulations.
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