I think Kairon is the most accurate about this, but I'm not certain. My brain feels fried right now. For some reason, I thought that Nintendo wound up with about 60-70% of the Rare's stock, which they bought after their initial investment, but I'm really not sure of it. I really haven't put much thought on the subject until now, but I recall that Nintendo basically sold their stake for $300 million.
Looking back, it seemed like Rare had wanted the chance to develop for other systems, especially after that e-Christmas card they sent out, which had an Xbox-like decorated box, along with others I can't specifically recall details about. My guess is that they had been in talks with Nintendo about being bought up entirely for some time, but also in talks with Microsoft at the same time about selling the remaining stake of themselves to MS. My guess is that Nintendo wanted to keep the amount of shares they owned, but Rare, perhaps exclusively under Stamper bros. influence here, probably wanted to be free from company influence or become a second party, seeing either direction as a more profitable path than the one they were on then.
Eventually, Nintendo probably became frustrated with both Rare's work and their attitude, so they just decided to drop the company. The Stamper bros. quickly bought Nintendo's shares back, and odds are, told Microsoft that Rare could be MS's entirely, odds are, leaving MS with a short deadline. Due to this deadline and just time delay issues that seem to be common practice with stock, the act of Nintendo selling Rare its own stock, and Microsoft purchasing all of Rare probably happened so close together that the stories blended together, and between the shock and the two console makers involved, the story didn't get delved into too far.
Up to this point, pretty much everything I've said has been speculation, and pretty much irrelevant to Monolith Soft. Now for the stuff that applies to Xenosaga and Baten Kaitos.
Of course, Nintendo was the publisher of all of Rare's titles while Rare was under the influence of Nintendo. That's why Banjo Kazooie and the rest won't be going to either the Virtual Console nor Xbox Live Arcade anytime soon without some sort of agreement. See, Nintendo is the only company with the right to print new copies of these games. However, the contents of these games belong to Rare, and by extension, Microsoft. It leaves them at a stalemate, as neither company can do anything with the games published by Nintendo without both companies approval. Conker's Bad Fur Day was not published by Nintendo, which is the reason why it could be remade and released on the Xbox.
The same will apply to Xenosaga and Baten Kaitos. With Xenosaga, Episode One was published by Namco, Ep. 2 was published by Namco in North America and Japan, but published by SCEE in Europe, and Ep. 3 was published by Namco Bandai. Now, considering Namco and Nintendo are not enemies, it is possible that Namco will either publish future editions of these three games exclusively for the Wii and/or other Nintendo platforms, or Namco might sell the publishing rights to Nintendo or Monolith soft. Either one is likely to happen, though it seems like Namco isn't too enthusiastic about the series anymore, so odds are they'll sell the rights to publish it to Nintendo. I skipped over mentioning who owns the Xenosaga property, because this is slightly less certain. What I gather from Wikipedia is that Monolith Soft is the sole creator of the IP, though they were owned by Namco at the time. If I understand things correctly, Monolith should retain the rights to the series, because they are identified as their own studio, and it even seems like Tetsuya may own or have owned part of the studio at some time. I don't think the IP could transfer ownership without total Namco's ownership of the studio, which I don't believe ever happened. That means that new entities in the Xenosaga series can still be created by Monolith soft. I also have to question whether or not Europe will be able to see a re-release of the second episode, seeing as who the publisher is, but I imagine, given the circumstances of the game's publishing, SCEE's contract may have been limited.
As for Baten Kaitos, I have to say that this property is alarmingly more complicated. The first game was published by Namco, so the same publishing issues take place as above. However, as Kairon has said, the game is co-developed by tri-Crescendo. Tri-Crescendo is a private studio, and isn't owned by Namco. They're more widely known as the sound designers of Valkyrie Profile, which, FYI, Square Enix published (Just to show you they aren't owned by Namco). Tri-Crescendo did work on both games, and though both games are credited mostly to Monolith Studios, I'd imagine that tri-Crescendo still owns part of the IP involved. A scenario that could occur from this type of effort could be that Baten Kaitos could be reproduced with tri-Crescendo's materials redone differently, using none of the original code. A better scenario is that tri-Crescendo could agree to work with Nintendo and Monolith Soft in all regards of remakes and the like. The second Baten Kaitos game was actually published by Nintendo, so there are no problems in this regard, but still, tri-Crescendo did work on the game, so again, issues with remakes and the like may be subject to their approval. Of course, let me say that tri-Crescendo seems to mostly do sound work, and it's possible that both games would be in fair-use in reproduction if all the music and sound effects were completely redone, which is possible.
Anyways, that's about it, most of my info is from Wikipedia, so you may want to take it with a grain of salt, but it sounds like it makes sense. Tri-Crescendo used to be a part of tri-Ace, but apparently they are their own company now, I'm not too clear on all of the details. Anyways, overall, I have to say that Namco will probably sell all the publishing rights of all four games they the rights of to Nintendo, and we'll probably see remakes of the games at some point in time, though I imagine it will be some time for any Baten Kaitos remake. It seems too soon for that.