Here's what I know about the contracts. I'll try to explain it as best I can.The Top 12 all sign "representation" deals. They enter a 50/50 partnership with 19 Entertainment. The 11 and 12th place finishers contract expires 90 days after the end of the show. So 90 days from now Lindsay and Mikalah will likely be released from their contract.
The Top 10 are contractually bound to do the AI tour. They are also obligated to do anything else AI askes of them during their contract period. For contestants 2-10 the contract expires 90 days after the tour concludes.
19 Entertainment has pre-arranged a recording contract for the winner.
Here's where the contract gets confusing. At any time during the contract period or duing the 90 day "option" period 19 Entertainment can extend the original contract. Without suing there is no "out" for the talent.
Clay, Diana DeGarmo and Tamyra Gray were all optioned by 19 Entertainment. Clay successfully sued to get out of his deal.
If 19 Entertainment "drops" you at the end of the options period you are free to do what ever you want. In reality 19 Entertainment seems to option anyone they think has a shot even if it's only to prevent them from signing on with someone else.
I hope I explained it ok. I'm used to dealing with talent contracts but I tried to simplify it as much as possible. My description isn't 100% legally accurate but it does give a general idea of what they contracts are like. The contract I saw was from season 2 so I'm sure things have changed. I'd bet the gist is the same since it was a really sweet deal for 19 Entertainment.
IMO because it is a 50/50 deal, in a lot of cases it may be better to hope that 19 drops representation.
The best case for Bo really would be to come in #2, have 19 drop him and then get a different management deal that doesn't take a 50% cut. Clive Davis pretty much publicly gave him a deal record deal so it's unlikly that 19 Entertainment would let him go.