What was there first: the spin or the morphology?
This plot is taken from Teklu et al. (2015). Here we adopted the classification of simulated galaxies from a run with baryons in a dark matter only run. There is a dichotomy in the spin parameter between disks and elliptical galaxies even in the dark matter only run!
The conclusion: The spin of the dark matter already decides whether the baryons will form a disk or an elliptical galaxy.