  We study the scaling relations between gas-phase metallicity, stellar mass
surface density ($\Sigma _*$), star formation rate surface density ($\Sigma
_{SFR}$), and molecular gas surface density ($\Sigma_{H_2}$) in local
star-forming galaxies on scales of a kpc. We employ optical integral field
spectroscopy from the MaNGA survey, and ALMA data for a subset of MaNGA
galaxies. We use Partial Correlation Coefficients and Random Forest regression
to determine the relative importance of local and global galactic properties in
setting the gas-phase metallicity. We find that the local metallicity depends
primarily on $\Sigma _*$ (the resolved mass-metallicity relation, rMZR), and
has a secondary anti-correlation with $\Sigma _{SFR}$ (i.e. a
spatially-resolved version of the 'Fundamental Metallicity Relation', rFMR). We
find that $\Sigma_{H_2}$ is less important than $\Sigma_{SFR}$ in determining
the local metallicity. This result indicates that gas accretion, resulting in
local metallicity dilution and local boosting of star formation, is unlikely to
be the primary origin of the rFMR. The local metallicity depends also on the
global properties of galaxies. We find a strong dependence on the total stellar
mass ($M_*$) and a weaker (inverse) dependence on the total SFR. The global
metallicity scaling relations, therefore, do not simply stem out of their
resolved counterparts; global properties and processes, such as the global
gravitational potential well, galaxy-scale winds and global
redistribution/mixing of metals, likely contribute to the local metallicity, in
addition to local production and retention.
