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)
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