Shadowmourne is lengthy because of the shard-gathering part.
The quest chain starts with "The Sacred and the Corrupt"
http://www.wowhead.com/quest=24545 And since they nerfed the number of souls you need for "A Feast of Souls" from 1000 to 50 (holy nerf batman), you can, in theory, go from the first step through the infusions in one night if you come prepared your raid is patient enough to do things in a particular order and wait for you to turn in quests between bosses. For details on the specifics of the quests and the infusions, just follow the wowhead links that lead from The Sacred and The Corrupt. Or PM me and I'll explain it, but it's a lot of typing for people that might not care to read wall of text.
THEN comes the grind. You have to get 50 shadowfrost shards. They drop like Val'anyr fragments, off of 25-man bosses, and NOT 100% (Not even from Lich King). And as far as anyone has reported, the droprate has not been buffed (though they have a higher droprate than Val'anyr fragments did and there is an even higher chance for them to drop off of heroic bosses as opposed to normal). It will take weeks if you are lucky and more likely a couple of months or more.
Then you get a quest to kill the lich king. He will drop a chest, lootable by ONLY THE PERSON ON THE QUEST, regardless of master looter. This starts a quest which you turn in to Mograine, when allows you to get the five quest-starter items that lead to the eventual rewards. These five quest-starters are still BoP to whomever had the Shadowmourne quest, but the rewards, as we know, are BoE.
Once a player turns in the Sealed Chest, it will not drop again for that player, regardless of whether or not they abandon the final quest to kill the Lich King. And since the chest is BoP-Unique, you can't just put off turning it in to get multiples (aside from the fact that you most likely couldn't repeat the sealed chest quest anyway, the same way you can't repeat Ony/Nef head quests). If multiple people are on the quest to kill the Lich King, a Chest will drop for each of them.