They haven't really updated much of it, it's still known as the 13th Black Crusade, it was also mentioned in the Dawn of War 2 Retribution...
The following is uninformed and half-hearted opinion. If I get things wildly wrong, please remember that this is more sleep-deprived ramblings than a truly insightful tactical analysis. That said: I think we should start by assessing what each would likely do. Abaddon's Black Crusades seem more about looting everything than permanently occupying the galaxy, so I suspect he'd push the advantage if he had it, but retreat if things start looking bad, possibly in the hopes of taking advantage of this temporary distraction tying up 3 of his enemies elsewhere. Eldrad probably has some greater sense of the strands of fate that would lead him to some decision we can't fathom, but assuming the defeat of any given champion won't doom the galaxy later on, he's likely to try and manipulate Gazghkull into fighting one of the others. Unless the fight is by his design, he would likely also attempt to retreat, as he probably wouldn't want to take on any of these veteran warriors in a fight he hasn't had a chance to rig in his favour. Abaddon might try to manipulate Gazghkull as well, and I'm uncertain which one would win in that respect. Abaddon has Slaanesh on his side but the Eldar are renowned for their ability to play enemies off against each other. Gazghkull's own motivations are simple enough to deduce: He wants to stomp things til they explode. I don't think he'd put up much resistance against being goaded to fight one enemy over another, so long as it makes a satisfying crunch when hit. I'm going to assume for no special reason that Eldrad is able to take control of Gazghkull. He's likely to sic him on Abaddon, reasoning that Abaddon is the most likely to flee besides himself, and likely wanting to bloody him a bit while he has the chance. Also, of all the people who could win, Eldrad would likely consider Abaddon's victory the least desirable, as Eldrad's soul would be in jeopardy. Whatever escape clause he might have planned for his own death, it probably isn't going to mean much with his body in the hands of the Warmaster of Chaos. Magneus isn't likely to be manipulated so easily, and with three high-priority targets in front of him, he would probably be reasonable in his choice. Being a clever man, he would likely see what Eldrad is trying to do, and choose between engaging Eldrad while Abaddon is busy with Gazghkull, or teaming up on either Abaddon or Gazghkull. I suspect he would ignore Eldrad, preferring a fair chance of one enemy of the Imperium dying over a slim chance of two or three dying. As for Magneus' choice between Gazghkull and Abaddon, I think it would make the most sense for him to go after Abaddon. If Gazghkull is dying and Magneus looks set to beat Abaddon, Abaddon is likely to retreat and escape 'justice'. Gazghkull is unlikely to retreat unless he's clearly winning by a wide margin. With Magneus and Gazghkull briefly teaming up on Abaddon, Eldrad has a decent window to escape, but with his absence Abaddon will now have a much easier time controlling Gazghkull. If he gets a chance, he will likely sic Gazghkull on Magneus instead of himself. From here, Magneus and Abaddon play a game of trying to manage 'Gazghkull aggro' while whittling down each other's considerable defences. Gazghkull, meanwhile, is likely having the the time of his life. Since manipulating orks probably isn't covered in the Codex Astartes, Abaddon will probably have Gazghkull on his side. I suspect this spells the end of Magneus, sadly. At least he went out like a true Space Marine. He can probably look forward to being canonized or something. With Magneus' death, Abaddon is likely rewarded by his Gods something fierce, but Gazghkull is probably also empowered by the Waaagh! The ensuing clash of the titans would simply be too close to call. At this point, even if Abaddon starts losing and tries to escape, Gazghkull is unlikely to let him leave. You may as well flip a coin on this one. Meanwhile, Eldrad is deploying massive raids against Ultramarine-protected Imperial territory.
No no, if Mat Ward had any thing to do with it, surely Abaddon would be roaming Tera pwning every thing and carving his name on the heart of the rotten corpse that sits on the Golden Throne!
Eldrad planned out how to kill Fulgrim, did that work? Nope. Fulgrim's now a daemon prince, Eldrad had a chance to stop him before he fully fell to chaos, but Eldrad failed in doing so.
Abaddon. Sickeningly powerful and underrated. Calgar would get swept aside. Eldrad... wouldn't really stand much of a chance 1v1 against either of Abaddon or Thrakka. I don't think his farseer abilities would have much affect on the warp resistance of Thrakka or Abaddon and his chaos blessings. So it really just comes down to Thrakka and Abaddon... and that sword. I think Thrakka would be cut to ribbons. Abaddon would certainly be badly dented/bruised/battered, but he'd still shred the greenskin pretty convincingly.
