The observational result that motivates the conclusions in this paper is illustrated in Figure3: Samples now of hundreds of galaxies show: The continuous parameter sequence defined by Sphs and by the disks (but not bulges) of S0 galaxies is indistinguishable from the parameter sequence defined by Magellanic irregular (Im) galaxies and by the disks (but not bulges) of spiral galaxies. This result was first found for dwarf galaxies by Kormendy (1985, 1987). Kormendy & Bender (2012) extend it to the highest-luminosity S and S0 disks.
The most robust conclusion is that Sph galaxies+S0 disks are related to Im galaxies+S galaxy disks. Both together are fundamentally different from classical bulges and ellipticals. This conclusion is also based on additional results that are not included in structural parameter correlations; one is that S+S0 disks are flat, whereas bulges+ellipticals are essentially three-dimensional. Understanding the above similarities and differences requires interpretation, but that interpretation now seems comfortably secure: (1) Bulges+elliptical galaxies form via major mergers, whereas disks+Im+Sph galaxies form by cold gas accretion. And more directly from Figure 3: (2) Sphs+S0 disks are transformed - i.e., star-formation-quenched - "red and dead" versions of Im galaxies+S galaxy disks.
Figure 3. Figure 2 parameter correlations with disks of Sa-Im galaxies added as blue points. When bulge-disk decomposition is necessary, the two components are plotted separately. Disks are not corrected to face-on orientation. The blue points represent 407 galaxes from 14 sources listed in the keys. From Kormendy & Bender (2012): They conclude that structural parameter correlations for Sa-Im galaxy "disks" are almost identical to those for S0-Sph "disks". This confirms conclusions in Kormendy (1985, 1987) using a large galaxy sample.