We analyze a suite of 33 cosmological simulations of the evolution of Milky Way-mass galaxies in low-density environments. Our sample spans a broad range of Hubble types at z=0, from nearly bulgeless disks to bulge-dominated galaxies. Despite the fact that a large fraction of the bulge is typically in place by z=1, we find no significant correlation between the morphology at z=1 and at z=0. The z=1 progenitors of disk galaxies span a range of morphologies, including smooth disks, unstable disks, interacting galaxies and bulge-dominated systems. By z=0.5, spiral arms and bars are largely in place and the progenitor morphology is correlated with the final morphology. We next focus on late-type galaxies with a bulge-to-total ratio B/T<0.3 at z=0. These show a correlation between B/T at z=0 and the mass ratio of the largest merger at z<2, as well as with the gas accretion rate at z>1. We find that the galaxies with the lowest B/T tend to have a quiet baryon input history, with no major mergers at z<2, and with a low and constant gas accretion rate that keeps a stable angular-momentum direction. More violent merger or gas accretion histories lead to galaxies with more prominent bulges. Most disk galaxies have a bulge Sersic index n<2. The galaxies with the highest bulge Sersic index tend to have histories of intense gas accretion and disk instability rather than active mergers.
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