In this work, we study the evolution of the mass-metallicity relations (MZRs) as predicted by the GAlaxy Evolution and Assembly (GAEA) semi-analytic model. We contrast these predictions with recent results from the VANDELS survey, that allows us to expand the accessible redshift range for the stellar MZR up to $zsim3.5$. We complement our study by considering the evolution of the gas-phase MZR in the same redshift range. We show that GAEA is able to reproduce the observed evolution of the $z<3.5$ gas-phase MZR and $z<0.7$ stellar MZR, while it overpredicts the stellar metallicity at $zsim3.5$. Furthermore, GAEA also reproduces the so-called fundamental metallicity relation (FMR) between gas-phase metallicity, stellar mass and star formation rate (SFR). In particular, the gas-phase FMR in GAEA is already in place at $zsim5$ and shows almost no evolution at lower redshift. GAEA predicts the existence of a stellar FMR, that is, however, characterized by a relevant redshift evolution, although its shape follows closely the gas-phase FMR. We also report additional unsolved tensions between model and data: the overall normalization of the predicted MZR agrees with observations only within $sim$0.1 dex; the largest discrepancies are seen at $zsim3.5$ where models tend to slightly overpredict observed metallicities; the slope of the predicted MZR at fixed SFR is too steep below a few ${rm M}_odot {rm yr}^{-1}$. Finally, we provide model predictions for the evolution of the MZRs at higher redshifts, that would be useful in the context of future surveys, like those that will be performed with JWST.
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