We selected a mass-limited sample of 4048 objects from the VIMOS VLT Deep Survey in the redshift interval 0.5<z<1.3. We used the amplitude of the 4000 Balmer break (Dn4000) to separate the galaxy population and the EW[OII]3727 line as proxy for the star formation activity. We discuss to what extent stellar mass drives galaxy evolution, showing for the first time the interplay between stellar ages and stellar masses over the past 8Gyr. Low-mass galaxies have small Dn4000 and at increasing stellar mass, the galaxy distribution moves to higher Dn4000 values as observed in the local Universe. As cosmic time goes by, we witness an increasing abundance of massive spectroscopically ET systems at the expense of the LT systems. This spectral transformation is a process started at early epochs and continuing efficiently down to the local Universe. This is confirmed by the evolution of our type-dependent stellar mass function. The underlying stellar ages of LT galaxies apparently do not show evolution, likely as a result of a continuous formation of new stars. All star formation activity indicators consistently point towards a star formation history peaked in the past for massive galaxies, with little or no residual star formation taking place in the most recent epochs. The activity and efficiency of forming stars are mechanisms that depend on stellar mass, and the mass assembly becomes progressively less efficient in massive systems as time elapses. The concepts of star formation downsizing and mass assembly downsizing describe a single scenario that has a top-down evolutionary pattern. The role of (dry) merging events seems to be only marginal at z<1.3, as our estimated efficiency in stellar mass assembly can possibly account for the progressive accumulation of passively evolving galaxies.
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