This is a purely hypothetical question which is not in any way important, but I’m simply curious about it: what would happen if I would install two different greeters on my computer? How would the computer do which one it should call on when it has finished booting and is supposed to show me a login screen next?
Nothing…
You’ll be asked which you want to use, and that will be the one that is running/used.
This install I’m using has gdm3, lightdm and sddm installed without issue, but I’ve opted to use sddm thus its the one that is run, and thus any configs I have setup for lightdm or gdm3 are ignored, as only sddm configs are used.
FYI: I didn’t install each of them, my install is a multi-desktop install meaning I installed one flavor, then added other flavor desktops to the install via the Ubuntu team’s metapackages; my choices caused the various DM/greeters I mentioned to be installed as dependencies. By nothing I meant there was no ill effect, I was just asked which I wanted to use each time I added a package that caused another DM to be installed.