It has been widely claimed that several lines of observational evidence point towards a ‘downsizing’ of the process of galaxy formation over cosmic time. This behaviour is sometimes termed ‘antihierarchical’, and contrasted with the ‘bottom-up’ (small objects form first) assembly of the dark matter structures in cold dark matter (CDM) models. In this paper, we address three different kinds of observational evidence that have been described as ‘downsizing’: the stellar mass assembly (i.e. more massive galaxies assemble at higher redshift with respect to low-mass ones), star formation rate (SFR) (i.e. the decline of the specific star formation rate is faster for more massive systems) and the ages of the stellar populations in local galaxies (i.e. more massive galaxies host older stellar populations). We compare a broad compilation of available data sets with the predictions of three different semi-analytic models of galaxy formation within the ΛCDM framework. In the data, we see only wea
