  We present a new semi-analytical model of galaxy formation, GECO (Galaxy
Evolution COde), aimed at a better understanding of when and how the two
processes of star formation and galaxy assembly have taken place. Our model is
structured into a Monte Carlo algorithm based on the Extended Press-Schechter
theory, for the representation of the merging hierarchy of dark matter halos,
and a set of analytic algorithms for the treatment of the baryonic physics,
including classical recipes for the gas cooling, the star formation
time-scales, galaxy mergers and SN feedback. Together with the galaxies, the
parallel growth of BHs is followed in time and their feedback on the hosting
galaxies is modelled. We set the model free parameters by matching with data on
local stellar mass functions and the BH-bulge relation at z=0. Based on such
local boundary conditions, we investigate how data on the high-redshift
universe constrain our understanding of the physical processes driving the
evolution, focusing in particular on the assembly of stellar mass and on the
star formation history. Since both processes are currently strongly constrained
by cosmological near- and far-IR surveys, the basic physics of the Lambda CDM
hierarchical clustering concept of galaxy formation can be effectively tested
by us by comparison with the most reliable set of observables. Our
investigation shows that when the time-scales of the stellar formation and mass
assembly are studied as a function of dark matter halo mass and the single
galaxy stellar mass, the 'downsizing' fashion of star formation appears to be a
natural outcome of the model, reproduced even in the absence of the AGN
feedback. On the contrary, the stellar mass assembly history turns out to
follow a more standard hierarchical pattern progressive in cosmic time, with
the more massive systems assembled at late times mainly through dissipationless
mergers.
