Yes, the team he is traded to owns the contract. AND IS BOUND BY THE TERMS OF THE TRADE ONCE APPROVED BY THE LEAGUE OFFICE.
According to the league, each trade is taken on a case by case basis. So if the Packers added language to the trade agreement stipulating extra compensation in the event of another trade of Favre to the Vikings and the league signed off on it, the team in question would have to comply.
From the link:
A popular subject contained in various e-mails we've received over the course of the day is a trade of Favre to a team other than the Vikings or the Bears, followed by a trade of Favre to a team like the Vikings or the Bears.
Don't count on it happening. Our guess is that the Packers would include in any trade of Favre to someone other than the Vikings or the Bears a provision that, if Favre thereafter is traded to the Vikings or the Bears, the compensation will increase to a first-round pick, or more.
Though the Packers can't release Favre with an understanding that he won't sign with certain teams, the Packers presumably can condition compensation on what the team that acquires Favre's rights does with them.
It's no different than, for example, the trade that gave the Broncos a seventh-round pick that would have upgraded if Jake Plummer had reported to the Bucs. Or the deal that will send a fourth-round pick from Tennessee to Dallas if Pacman Jones isn't reinstated for the 2008 season.
It's a conditional draft pick — and the condition that would increase the compensation in the case of a Favre trade would be the re-trading of Favre to a team like the Bears or the Vikings.
We asked NFL spokesman Greg Aiello whether such a term would be enforceable, but Aiello declined to speculate. He said that the trades are considered on a case-by-case basis, and that the league office would evaluate the terms that are presented, if/when trade terms are reached.
Peace.