Thanks for writing, Findra! Before I talk about how to break your alliance, I'd like to rudely second-guess you for a moment. Are you sure this is the right thing to do? It's great that you have enough people to raid on your own -- however, that does not mean you always will. This is a sensitive time for Warcraft players. In the northern hemisphere, summer is upon us, which means many players cut back their playtime to enjoy the warm weather, go on vacations, and so on (although it can also mean an influx of school-age applicants).
Also, we've seen the last of the new content from The Burning Crusade, and no one knows when the next expansion will go live, although the safe money is on a fourth-quarter 2008 launch, or even later. My guild has already lost a few players who have quit the game indefinitely while Blizzard cooks up some new content. You're going to see more and more people fed up paying that monthly fee without any major patches forthcoming, and even more people who are just flat-out bored with the game.
So my point here is to be cautious. You could lose a few members and be back to square one in a heartbeat. And if you don't have that alliance to fall back on, you won't be running anything, which could lead to losing more members in a slow downward spiral.
Sometimes in this situation you can have your cake and eat it too. You could compromise by running new dungeons with your allied guild while farming the old dungeons on your own. This gives you the benefit of drawing on a larger player pool when you need more well-geared toons or specific class makeups for an encounter you're still learning. At the same time, you'll be able to hoard the easily farmed loot for your own people. Whether or not your allies will go along with that plan is another story, but if it's that or nothing for them, they might not have any choice.
Still, none of this advice is anything you actually asked for, so I'll get down to business. If you want to break an alliance, the first thing you have to do is square it with your own members. Outline what's going to change as far as scheduling, filling slots, loot rules, etc. Then make sure they're comfortable with this decision. Most importantly, check that most of the people who are raiding now plan to continue raiding in the future.
Timing is critical. Don't think that the other guild's officers aren't /who'ing your guild from time to time to see what you guys are up to. If they do that one night and see 25 people in Black Temple, you just blew it. At that point they can't help but feel deceived. It's like if some friends tell you they're busy with homework tonight but then you run into them at the movie theater. So make sure you approach the other guild before you run something on your own.
I'd also recommend limiting the conversation to a one-on-one between your guild or raid leader and their guild or raid leader. I've had alliance officer meetings in the past where a bunch of us met with a bunch of them. Usually this is a bad idea. It's a far more tense conversation. With so many people typing in chat at one time, it can be difficult to follow the different threads of the conversation. You have three people talking about loot, four people talking about finding more tanks, one person commenting on what he's watching on TV, and another person trying to get everyone on the same topic -- and failing miserably. (That's why I recommend using a voice-chat server for large meetings like this). Not to mention, all it takes is one person to say something inflammatory or patronizing and the meeting can quickly devolve into finger-pointing and name-calling.
For all of these reasons, it's much better to make it a personal conversation between two leaders. Before the meeting, each person should check in with the other officers about any outstanding issues they'd like to address. Afterward, you can each report back and then meet again if necessary to address any lingering concerns.
When you pull the plug, make sure you keep it open-ended and friendly. When an alliance ends because you've recruited enough to be self-sufficient, it usually means the alliance worked well. After all, if you weren't progressing, you probably wouldn't have had success recruiting. Don't burn this bridge -- you never know when you might need a certain niche filled for content of any size, and it's a real asset to be able to draw on another guild's player pool from time to time.
How do you keep it open-ended? Well, be honest but don't talk in absolutes. Say that you'd like to try running raids on your own but that it might not work out. Don't say you'll never raid with them again, because one day you might.
Don't point out their faults. Rather, emphasize what you liked about their guild. Wish them success in the future. Above all, realize that this is a sensitive moment and that what you say here may determine whether your guilds continue to be on good terms or not.
Once the conversation is over, don't discuss it with anyone else from their guild. Tell them to refer any queries to the officer you've been talking to so he or she can discuss it with you. The wost thing you can do is talk to different people and give them different information because you can't remember exactly what you said to the first person. After that, the worst thing you can do is start giving all your reasons and rationale to any member who whispers you. Their officers might have spun the circumstances in their own way, and by talking to their members you could undo their efforts. Unless you want to find yourself smack dab in the middle of another guild's drama, exercise some professional courtesy.
You do have one distinct advantage in breaking the alliance now, because virtually any guild will be able to field enough players to run the entire 10-player raiding path in Wrath of the Lich King. I guess that brings up an interesting question: When WotLK launches, will raiding alliances be a thing of the past?