  We demonstrate the existence of a -local- relation between galaxy surface
mass density, gas metallicity, and star-formation rate density using
spatially-resolved optical spectroscopy of HII regions in the local Universe.
One of the projections of this distribution, -the local mass-metallicity
relation- extends over three orders of magnitude in galaxy mass density and a
factor of eight in gas metallicity. We explain the new relation as the combined
effect of the differential radial distributions of mass and metallicity in the
discs of galaxies, and a selective star-formation efficiency. We use this local
relation to reproduce -with remarkable agreement- the total mass-metallicity
relation seen in galaxies, and conclude that the latter is a scale-up
integrated effect of a local relation, supporting the inside-out growth and
downsizing scenarios of galaxy evolution.
