We study the evolution of 82302 star-forming (SF) galaxies from the SDSS. Our main goals are to explore new ways of handling star formation histories (SFH) obtained with our publicly available spectral synthesis code STARLIGHT, and apply them to investigate how SFHs vary as a function of nebular metallicity (Zneb). Our main results are: (1) A conventional correlation analysis shows how global properties such as luminosity, mass, dust content, mean stellar metallicity and mean stellar age relate to Zneb. (2) We present a simple formalism which compresses the results of the synthesis into time-dependent star formation rates (SFR) and mass assembly histories. (3) The current SFR derived from the population synthesis and that from H-alpha are shown to agree within a factor of two. Thus we now have a way to estimate SFR in AGN hosts, where the H-alpha method cannot be applied. (4) Fully time-dependent SFHs are derived for all galaxies and averaged over six Zneb bins spanning the entire SF wing in the [OIII]/H-beta X [NII]/H-alpha diagram. (5) We find that SFHs vary systematically along the SF sequence, such that low-Zneb systems evolve slower and are currently forming stars at a higher relative rate. (6) At any given time, the distribution of specific SFRs for galaxies within a Zneb-bin is broad and roughly log-normal. (7) The same results are found grouping galaxies in stellar mass (M*) or surface mass density (S*) bins. (8) The overall pattern of SFHs as a function of Zneb, M* or S* is robust against changes in selection criteria, choice of evolutionary synthesis models for the spectral fits, and differential extinction effects. (Abridged)
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