Context :

Aims : There are two aims to our analysis .
On the one hand we are interested in addressing whether a sample of morphologically selected early-type galaxies ( ETGs ) 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 \leq z \leq 2.5 .

Methods : From the 1302 galaxies brighter than Ks ( AB ) =22 selected from the GOODS-MUSIC catalogue , we classified the ETGs , i.e .
elliptical ( E ) and spheroidal galaxies ( E/S0 ) , on the basis of their morphology and the passive galaxies on the basis of their specific star formation rate ( sSFR \leq 10 ^ { -11 } yr ^ { -1 } ) .
Since the definition of a passive galaxy depends on the model parameters assumed to fit the spectral energy distribution of the galaxy , in addition to the assumed sSFR threshold , we probed the dependence of this definition and selection on the stellar initial mass function ( IMF ) .

Results : We find that spheroidal galaxies can not be distinguished from the other morphological classes on the basis of their low star formation rate , irrespective of the IMF adopted in the models .
In particular , we find that a large fraction of passive galaxies ( > 30 % ) are disc-shaped objects and that the passive selection misses a significant fraction ( \sim 26 % ) of morphologically classified ETGs .
Using the sample of 1302 galaxies morphologically classified into spheroidal galaxies ( ETGs ) and non-spheroidal galaxies ( LTGs ) , we find that the fraction of these two morphological classes is constant over the redshift range 0.6 \leq z \leq 2.5 , being 20-30 % the fraction of ETGs and 70-80 % the fraction of LTGs .
However , at z < 1 these fractions change among the population of the most massive ( M _ { * } \geq 10 ^ { 11 } M _ { \odot } ) galaxies , with the fraction of massive ETGs rising up to 40 % and the fraction of massive LTGs decreasing to 60 % .
Parallel to this trend , we find that the number density and the stellar mass density of the whole population of massive galaxies increase by almost a factor of \sim 10 between 0.6 \leq z \leq 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 both ETGs and LTGs ( M _ { * } > 3 - 4 \times 10 ^ { 11 } M _ { \odot } ) does not increase from z \sim 2.5 , contrary to the lower mass galaxies .
This suggests that 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 .

Conclusions :