  Assessments of the cold-gas reservoir in galaxies are a cornerstone for
understanding star-formation processes and the role of feedback and baryonic
cycling in galaxy evolution. Here we exploit a sample of 392 galaxies (dubbed
MAGMA, Metallicity and Gas for Mass Assembly), presented in a recent paper, to
quantify molecular and atomic gas properties across a broad range in stellar
mass, Mstar, from $\sim 10^7 - 10^{11}$ Msun. First, we find the metallicity
($Z$) dependence of alpha_CO to be shallower than previous estimates, with
alpha_CO$\propto (Z/Z_\odot)^{-1.55}$. Second, molecular gas mass MH2 is found
to be strongly correlated with Mstar and star-formation rate (SFR), enabling
predictions of MH2 good to within $\sim$0.2 dex. The behavior of atomic gas
mass MHI in MAGMA scaling relations suggests that it may be a third,
independent variable that encapsulates information about the circumgalactic
environment and gas accretion. If Mgas is considered to depend on MHI, together
with Mstar and SFR, we obtain a relation that predicts Mgas to within
$\sim$0.05 dex. Finally, the analysis of depletion times and the scaling of
MHI/Mstar and MH2/Mstar over three different mass bins suggests that the
partition of gas and the regulation of star formation through gas content
depends on the mass regime. Dwarf galaxies tend to be overwhelmed by (HI)
accretion, while for galaxies in the intermediate Mstar "gas-equilibrium" bin,
star formation proceeds apace with gas availability. In the most massive
"gas-poor, bimodality" galaxies, HI does not apparently participate in star
formation, although it generally dominates in mass over H2. Our results confirm
that atomic gas plays a key role in baryonic cycling, and is a fundamental
ingredient for current and future star formation, especially in dwarf galaxies.
(abridged for arXiv)
