  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.
