Well, okay, the title of this thread is actually somewhat misleading, for reasons that I'll address shortly.
It's common knowledge that Family Guy evolved from the
Larry and Steve shorts that Seth MacFarlane developed for Cartoon Network. Fox was impressed enough with MacFarlane's work to offer him the opportunity to pitch a show for them, and the rest is history.
However, what if Fox never approached MacFarlane, and something like Family Guy is instead created for Cartoon Network? It was, after all, the network that MacFarlane had already had a connection with.
Now, I imagine that the resulting cartoon will probably be somewhat closer to Larry and Steve than Family Guy was IOTL, but otherwise, how might this version of the program looked? Mind you, Family Guy premiered several years before Cartoon Network created Adult Swim, so even if it airs in the evenings, the show probably won't exceed Space Ghost Coast to Coast/Ren and Stimpy levels of raunchiness, at least initially. Would such a program be more likely to avoid the struggles that Family Guy faced on Fox, potentially avoiding cancellation? How might Seth MacFarlane's career (keep in mind all of the shows that he's had some sort of hand in) have gone differently had his signature program debuted on Cartoon Network rather than Fox?