From this little corner of the internet, it looks to me like there are three main possibilities. Basically, one party could buy the other partner out, the Dodgers might be sold to a third party, or Frank and Jamie might both retain an interest in the club.
It's hard to see Frank or Jamie having the financial wherewithal to buy the other out and still have enough money to run the Dodgers on their own. See, if Jamie's to be believed, the Dodgers account for $800 million of the couple's $1.2 billion estate. If everything's split up, neither partner would be able to take the other out without some serious outside financing help.
While that sort of thing might not be as hard as you think, it still ain't easy, especially if you believe the whispers that the McCourts needed some pretty heavy financing to buy the team in the first place. The money just might not be there for one party to buy out the other.
If this doesn't work out, the McCourts might sell the team to a third party. As you might have heard, the number of folks walking around with $800 million in their pockets is pretty darned low right now. And in the time it takes to find a suitable ownership group (presumably one that doesn't go nuclear on itself after 29.96 years of marriage), the Dodgers might have to be run on a shoestring. That's bad news for a team with World Series aspirations.
The third possibility in all this is that the McCourts keep their joint ownership in some way. This would require a great deal of creativity, as they can't, you know, stand each other right now. As a refresher, she cheated and he moved to cut her out of the fortune. Productive business partners, these two ain't.
But it could happen, if one or both agreed to step back from operations of the club. This doesn't seem all that likely, however. Frank enjoys being public about his role with the team, and you might recall that Jamie holds herself to be the "face of the Dodgers."
So what will happen? Well, we're all waiting to find out.