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We present results from SPH-cosmological simulations, includingself-consistent modelling of SN feedback and chemical evolution, of galaxiesbelonging to two clusters and twelve groups. We reproduce the mass-metallicity(ZM) relation of galaxies classified in two samples according to theirstar-forming activity, as parametrized by their sSFR, across a redshift rangeup to z=2.  Its slope shows irrelevant evolution in the passive sample, being steeper ingroups than in clusters. However, the sub-sample of high-mass passive galaxiesonly is characterized by a steep increase of the slope with redshift, fromwhich it can be inferred that the bulk of the slope evolution of the ZMrelation is driven by the more massive passive objects. (...ABRIDGED...)  The ZM relation for the star-forming sample reveals an increasing scatterwith redshift, indicating that it is still being built at early epochs. Thestar-forming galaxies make up a tight sequence in the SFR-M_* plane at highredshift, whose scatter increases with time alongside with the consolidation ofthe passive sequence. We also confirm the anti-correlation between sSFR andstellar mass, pointing at a key role of the former in determining the galaxydownsizing, as the most significant means of diagnostics of the star formationefficiency. Likewise, an anti-correlation between sSFR and metallicity can beestablished for the star-forming galaxies, while on the contrary more activegalaxies in terms of simple SFR are also metal-richer.  We discuss these results in terms of the mechanisms driving the evolutionwithin the high- and low-mass regimes at different epochs: mergers,feedback-driven outflows and the intrinsic variation of the star formationefficiency.

Evolution of the Mass-Metallicity relations in passive and star-forming galaxies from SPH-cosmological simulations