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[abridged] We quantify the morphological evolution of z~0 massive galaxies($M*/M_\odot\sim10^{11}$) from z~3 in the 5 CANDELS fields. The progenitors areselected using abundance matching techniques to account for the mass growth.The morphologies strongly evolve from z~3. At z<1, the population matches themassive end of the Hubble sequence, with 30% of spheroids, 50% of galaxies withequally dominant disk and bulge components and 20% of disks. At z~2-3 there isa majority of irregular systems (~60-70%) with still 30% of spheroids.  We then analyze the SFRs, gas fractions and structural properties for thedifferent morphologies independently. Our results suggest two distinct channelsfor the growth of bulges in massive galaxies.  Around 30-40% were already bulges at z~2.5, with low average SFRs andgas-fractions (10-15%), high Sersic indices (n>3-4) and small effective radii($R_e$~1 kpc) pointing towards an early formation through gas-rich mergers orVDI. Between z~ 2.5 and z~0, they rapidly increase their size by a factor of~4-5, become all passive but their global morphology remains unaltered. Thestructural evolution is independent of the gas fractions, suggesting that it isdriven by ex-situ events.  The remaining 60% experience a gradual morphological transformation, fromclumpy disks to more regular bulge+disks systems, essentially happening at z>1.It results in the growth of a significant bulge component (n~3) for 2/3 of thesystems possibly through the migration of clumps while the remaining 1/3 keepsa rather small bulge (n~1.5-2). The transition phase between disturbed andrelaxed systems and the emergence of the bulge is correlated with a decrease ofthe star formation activity and the gas fractions. The growth of the effectiveradii scales roughly with $H(z)^{-1}$ and it is therefore consistent with theexpected growth of disks in galaxy haloes.

The morphologies of massive galaxies from z~3 - Witnessing the 2 channels of bulge growth