We follow the galaxy stellar mass assembly by morphological and spectral type in the COSMOS 2-deg ^ { 2 } field .
We derive the stellar mass functions and stellar mass densities from z = 2 to z = 0.2 using 196,000 galaxies selected at F _ { 3.6 \mu m } > 1 \mu Jy with accurate photometric redshifts ( \sigma _ { ( z _ { phot } - z _ { spec } ) / ( 1 + z _ { spec } ) } = 0.008 at i ^ { + } < 22.5 ) .
Using a spectral classification , we find that z \sim 1 is an epoch of transition in the stellar mass assembly of quiescent galaxies .
Their stellar mass density increases by 1.1 dex between z = 1.5 - 2 and z = 0.8 - 1 ( \Delta t \sim 2.5 Gyr ) , but only by 0.3 dex between z = 0.8 - 1 and z \sim 0.1 ( \Delta t \sim 6 Gyr ) .
Then , we add the morphological information and find that 80-90 % of the massive quiescent galaxies ( log ( { \cal M } ) \sim 11 ) have an elliptical morphology at z < 0.8 .
Therefore , a dominant mechanism links the shutdown of star formation and the acquisition of an elliptical morphology in massive galaxies .
Still , a significant fraction of quiescent galaxies present a Spi/Irr morphology at low mass ( 40-60 % at log ( { \cal M } ) \sim 9.5 ) , but this fraction is smaller than predicted by semi-analytical models using a “ halo quenching ” recipe .
We also analyze the evolution of star-forming galaxies and split them into “ intermediate activity ” and “ high activity ” galaxies .
We find that the most massive “ high activity ” galaxies end their high star formation rate phase first .
Finally , the space density of massive star-forming galaxies becomes lower than the space density of massive elliptical galaxies at z < 1 .
As a consequence , the rate of “ wet mergers ” involved in the formation of the most massive ellipticals must decline very rapidly at z < 1 , which could explain the observed slow down in the assembly of these quiescent and massive sources .