My comments, or most likely, things I might add (aside to say I enjoyed this a lot, and will, if you continue!

) :
Many times these Primmadonnas have a good knowledge of the books, then the Diva players become, rather than Mary Sues, Canon Sues (you can guess, more or less what is a Canon Sue, think in the character of Arwen as she was portrayed in the movies, put them into a RP, and you have a good examples of Canon Sues -- Movies fans, take no offence).
And because this (because they might have some knowledge of the books) their Divism grows and is fed, for they will be continuously recalling the whole world how much good they are -- until they met another player that will amend them (just guess what will happen that day), for Divas adapt the books to their purposes and disregard what wouldn’t fit to them (*of course* Arwen fights and rules the Bruinen and will save Frodo’s day).
Really, it is more an OOC attitude than ICly, despite as it has been pointed out, it is very related to MS/CS, difficult characters so, many times, it is hard to distinguish them.
Divas need to be applauded, IC and OOC, so they tend to play important characters, and surely will expect to be OOC promoted. It is what they need the more, to be constantly told how much they rock and to have people drooling about and praising their posts, be they IC or OOC. For example, many of them write poetry (in sindarin, quenya, whatever) and will put it into their IC posts. It little matters if it has no IC sense. Even if they are in the middle of a battle like the Pelennor Fields, they will do. Their chars will take a halt and will start to sing. And the orcs will stop to listen to them.
Yes, they use to pay little attention to the others’ posts, and those of the admins, they use to be ignored. It is remarkable how much they can figure out they missed them. Or, sometimes, they will argue with the admins endlessly, honestly surprised that someone dared to amend them, since they are right. They are the ones that will amend the admins, because Divas are better, and how, than the admins, mods and even Tolkien himself (how did Tolkien to say –or not to say- this or that? Unacceptable, he surely forgot to mention it).
Sometimes they might brought questions, OOCly, saying that they need to know the reply and to deal about in order to post. They will be odd and hard questions, like “How many cousins does Frodo have, first second and third cousins?”. If they are told that it little matters or to skip that or simply that people around don’t know, they will insist that is basic to know it and then will post the answer as a gift -- and triumph (you never will know if they were right unless you get the fancy to check every book wrote by or about Tolkien).
To deal with them is almost impossible; but if their Divism has no deep roots (for example, if they played in boards were the quality level was, ahem, very low? and yours is high, and they realize it) there might be some hope. A way (the others have been already mentioned) is to try “block” the char ICly, it is very important to keep separate the IC and OOC life, but especially with these Primmadonnas. How to do it? Usually there is always a char keeping a higher position than theirs (lords/ladies, brothers, parents, husbands -- bring a Vala if need be!

). So you can shape the scene and to put the char in its place (then, don’t forget to warn the people, by PM or posting in a restricted forum, of what is going on, because last time I tried to do this I forgot to tell the people and obviously failed :P).
Anyway, if you want to get rid of Divas, the best way is to ignore them. They will leave at once -- remember, if they get no applauses, why would they stay?. They deigned themselves to visit your board and you paid them no attention, so, the board is not a worth place and they will seek for a board where their skills will be appreciated as they deserve.
Argh, I had not expected to write this much! *stops*
Nolen, lecturing as a Diva