We use ~8,600 >5e10 Msol COSMOS galaxies to study how the morphological mix of massive ellipticals, bulge-dominated disks, intermediate-bulge disks, bulge-less disks and irregular galaxies evolves from z=0.2 to z=1. The morphological evolution depends strongly on mass. At M>3e11 Msol, no evolution is detected in the morphological mix: ellipticals dominate since z=1, and the Hubble sequence has quantitatively settled down by this epoch. At the 1e11 Msol mass scale, little evolution is detected, which can be entirely explained with major mergers. Most of the morphological evolution from z=1 to z=0.2 takes place at masses 5e10 - 1e11 Msol, where: (i) The fraction of spirals substantially drops and the contribution of early-types increases. This increase is mostly produced by the growth of bulge-dominated disks, which vary their contribution from ~10% at z=1 to >30% at z=0.2 (cf. the elliptical fraction grows from ~15% to ~20%). Thus, at these masses, transformations from late- to early-types result in disk-less elliptical morphologies with a statistical frequency of only 30% - 40%. Otherwise, the processes which are responsible for the transformations either retain or produce a non-negligible disk component. (ii) The bulge-less disk galaxies, which contribute ~15% to the intermediate-mass galaxy population at z=1, virtually disappear by z=0.2. The merger rate since z=1 is too low to account for the disappearance of these massive bulge-less disks, which most likely grow a bulge via secular evolution.

5 pages, 3 figures, submitted to ApJL