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 \sim 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 \sim 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 Sérsic index n < 2 .
The galaxies with the highest bulge Sérsic index tend to have histories of intense gas accretion and disk instability rather than active mergers .