  The GalICS (Galaxies in Cosmological Simulations) semi-analytical model of
hierar- chical galaxy formation is used to investigate the effects of different
galactic properties, including star formation rate (SFR) and outflows, on the
shape of the mass metallic- ity relation and to predict the relation for
galaxies at redshift z=2.27 and z=3.54. Our version of GalICS has the chemical
evolution implemented in great detail and is less heavily reliant on
approximations such as instantaneous recycling. We vary the model parameters
controlling both the efficiency and redshift dependence of the SFR as well as
the efficiency of supernova feedback. We find that the factors controlling the
SFR influence the relation significantly at all redshifts and require a strong
redshift dependence, proportional to 1+z, in order to reproduce the observed
relation at the low mass end. Indeed, at any redshift, the predicted relation
flattens out at the high mass end resulting in a poorer agreement with
observations in this regime. We also find that variation of the parameters
associated with outflows has a minimal effect on the relation at high redshift
but does serve to alter its shape in the more recent past. We thus conclude
that the relation is one between SFR and mass and that outflows are only
important in shaping the relation at late times. When the relation is
stratified by SFR it is apparent that the predicted galaxies with increasing
stellar masses have higher SFRs, supporting the view that galaxy downsizing is
the origin of the relation. Attempting to reproduce the observed relation, we
vary the parameters controlling the efficiency of star formation and its
redshift dependence and compare the predicted relations with Erb et al. (2006)
at z=2.27 and Maiolino et al. (2008) at z=3.54 in order to find the
best-fitting parameters. (Abridged)
