  The aim of our analysis is twofold. On the one hand we are interested in
addressing whether a sample of ETGs morphologically selected differs from a
sample of passive galaxies in terms of galaxy statistics. On the other hand we
study how the relative abundance of galaxies, the number density and the
stellar mass density for different morphological types change over the redshift
range 0.6<z<2.5. From the 1302 galaxies brighter than Ks=22 selected from the
GOODS-MUSIC catalogue, we classified the ETGs on the basis of their morphology
and the passive galaxies on the basis of their sSFR. We proved how the
definition of passive galaxy depends on the IMF adopted in the models and on
the assumed sSFR threshold. We find that ETGs cannot be distinguished from the
other morphological classes on the basis of their low sSFR, irrespective of the
IMF adopted in the models. Using the sample of 1302 galaxies morphologically
classified into spheroidal galaxies (ETGs) and not spheroidal galaxies (LTGs),
we find that their fractions are constant over the redshift range 0.6<z<2.5
(20-30% ETGs vs 70-80% LTGs). However, at z<1 these fractions change among the
population of the most massive (M*>=10^(11) M_sol) galaxies, with the fraction
of massive ETGs rising up to 40% and the fraction of massive LTGs decreasing
down to 60%. Moreover, we find that the number density and the stellar mass
density of the whole population of massive galaxies increase almost by a factor
of ~10 between 0.6<z<2.5, with a faster increase of these densities for the
ETGs than for the LTGs. Finally, we find that the number density of the
highest-mass galaxies (M*>3-4x10^(11) M_sol) both ETGs and LTGs do not increase
since z~2.5, contrary to the lower mass galaxies. This suggests that the
population of the most massive galaxies formed at z>2.5-3 and that the assembly
of such high-mass galaxies is not effective at lower redshift.
