  We use cosmological hydrodynamic simulations to investigate how inflows, star
formation, and outflows govern the the gaseous and metal content of galaxies.
In our simulations, galaxy metallicities are established by a balance between
inflows and outflows as governed by the mass outflow rate, implying that the
mass-metallicity relation reflects how the outflow rate varies with stellar
mass (M*). Gas content is set by a competition between inflow into and gas
consumption within the ISM, the latter being governed by the SF law, while the
former is impacted by both wind recycling and preventive feedback. Stochastic
variations in the inflow rate move galaxies off the equilibrium M*-Z and
Z*-fgas relations in a manner correlated with star formation rate, and the
scatter is set by the timescale to re-equilibrate. The evolution of both
relations from z=3-0 is slow, as individual galaxies tend to evolve mostly
along the relations. Gas fractions at a given M* slowly decrease with time
because the cosmic inflow rate diminishes faster than the consumption rate,
while metallicities slowly increase as infalling gas becomes more enriched.
Observations from z~3-0 are better matched by simulations employing
momentum-driven wind scalings rather than constant wind speeds, but all models
predict too low gas fractions at low masses and too high metallicities at high
M*. All our models reproduce observed second-parameter trends of the
mass-metallicity relation with star formation rate and environment, indicating
that these are a consequence of equilibrium and not feedback. Overall, the
analytical framework of our equilibrium scenario broadly captures the relevant
physics establishing the galaxy gas and metal content in simulations, which
suggests that the cycle of baryonic inflows and outflows centrally governs the
cosmic evolution of these properties in typical star-forming galaxies.
