As a quick recap, nepotistic continuity is when a creator has characters from his/her previous works show up in his/her current works. You can usually tell when nepotistic continuity is at hand, because a story will involve an obscure plot point from an old comic, and even if you don't recall offhand who wrote that previous comic, odds are it was the writer of the current comic book.
Paternalistic continuity is when a creator is protective of a certain character, like Jim Starlin with Thanos.
Obligatory Continuity, however, differs from those other terms in that it is not really a voluntary action. The term occurred to me when I was talking with my pal Stony about how he felt Lex Luthor should be a better villain, because Batman has so many great villains, to which I joked, "Like Killer Croc!"
And it struck me - once a character has become "established," future writers are pretty much obligated to use the character eventually, no matter whether a writer would, under normal circumstances, ever actually WANT to use this character.
This is why we keep seeing Killer Croc show up in Batman comics. Seriously, no writer is saying, "Aw man, FINALLY, I get to write the Killer Croc story I've always wanted to tell!" No, it's just that Killer Croc has become "established," and therefore future writers are obligated to EVENTUALLY use him, whether they really have anything to say with him or not.
The same goes for Penguin, Riddler, Mysterio, Mr. Sinister, Apocalypse, Vulture, Electro, Doctor Octopus and others.
It doesn't matter whether creators really WANT to write about Mr. Sinister (because, well, really, who WANTS to write about Mr. Sinister? The guy is lameness on a stick), they're obligated to - and, surprise, surprise - the X-Books are having a summer crossover centered around none other than Mr. Sinister!
It's an obligation that writers have to deal with when taking on longterm properties, and it's an amusing one, I think.
It also leads to stuff like Peter David coming up with a rather (unintentionally, I think) hilarious origin for the Vulture, as he feels obligated to eventually revisit Spidey's rogues gallery, whether there is a story there or not.