  In order to understand galaxy growth evolution, it is critical to constrain
the evolution of its building block: gas. Mostly comprised by Hydrogen in its
neutral (HI) and molecular (H2) phases, the latter is the one mostly directly
associated to star-formation, while the neutral phase is considered the
long-term gas reservoir. In this work, we make use of an empirical relation
between dust emission at millimeter wavelengths and total gas mass in the
inter-stellar medium (M_HI plus M_H2) in order to retrieve the HI content in
galaxies. We assemble an heterogeneous sample of 335 galaxies at 0.01<z<6.4
detected in both mm-continuum and carbon monoxide (CO), with special focus on a
blindly selected sample to retrieve HI cosmological content when the Universe
was ~2-6Gyr old (1<z<3). We find no significant evolution with redshift of the
M_HI/M_H2 ratio, which is about 1-3 (depending on the relation used to estimate
M_HI). This also shows that M_H2-based gas depletion times are underestimated
overall by a factor of 2-4. Compared to local Universe HI mass functions, we
find that the number density of galaxies with M_HI>1E10.5M_sun significantly
decreased since 8-12Gyr ago. The specific sample used for this analysis is
associated to 20-50% of the total cosmic HI content as estimated via Damped
Lyman-alpha Absorbers. In IR luminous galaxies, HI mass content decreases
between z~2.5 and z~1.5, while H2 seems to increase. We also show source
detection expectations for SKA surveys.
