What determines the bulge to disk ratio of galaxies

Galaxies having the same luminosity may have very different bulge to disk ratios, while the mean bulge to disk ratio slowly increases with total luminosity (Schecter and Dressler, 1987, Sandage et al., 1985). Such a behavior is expected if ellipticals and the spheroidal components of disk galaxies are produced by secondary accretion of galaxies by larger galaxies. This is illustrated using a simple toy model of the evolution of the mass function of galaxies due to galaxy mergers