Are dry mergers of ellipticals the way to reconcile model predictions with downsizing?

Aims. We show that the bulk of the star formation and the galaxy assembly should occur simultaneously in order to reproduce at the same time the downsizing and the chemical properties of present-day massive spheroids within one effective radius. Methods. By means of chemical evolution models, we create galactic building blocks of several masses and different chemical properties. We then construct a sample of possible merger histories going from a multiple minor merger scenario to a single major merger event aimed at reproducing a single massive elliptical galaxy. We compare our results against the mass-[Mg/Fe] and the mass-metallicity relations. Results. We found that a series of multiple dry mergers (no star formation in connection with the merger) involving building-blocks that have been created ad hoc to satisfy the [Mg/Fe]-mass relation cannot fit the mass-metallicity relation and viceversa. A major dry merger, instead, does not make the agreement with observations worse if it happens between galaxies that already obey both the mass(s)-[Mg/Fe] and the mass(s)-metallicity relations. However, this process alone cannot explain the physical reasons for these trends. Conclusions. Dry mergers alone are not be the way to reconcile the need of a more efficient star formation in the most massive galaxies with the late-time assembly suggested in the hierarchical paradigm to recover the galaxy downsizing.