Let's say boxer A and B are signed to two promotional companies. Who decides which one gets the rights to hosting the event and card
It depends: If there's a purse bid the promoter who wins the purse bid. If there's a clear A side vs. B side fighter, almost always it's the promoter of the A side fighter Basically it's negotiated
Example: A side fighter is promoted by say, Top Rank. B side fighter is promoted by an outfit the size of Gary Shaw Promotions, Top Rank is likely gonna control the promotion, the smaller promotion will probably negotiate for some concessions for their fighter since they won't be controlling the show.
I think he may have been asking for clarity on the definition of A-side (guessing if they don't even know about purse bids they're pretty new to all things boxing) @B_irnmn1812 the "A-side" is the fighter with the more dominant profile in the sport, ie more famous/successful/popular (although not always necessarily all three of those). Usually they are the one that will draw more attention to an event, thus generate more profit for everyone, so they command more bargaining power overall. If there's only a slight imbalance, they go to a purse bid, or auction, where the promoter willing to pay more ultimately gets to be in charge.
With that being said if you're signed to a promoter does that mean you can't accepts fights from other promoters?
They're usually contracted (exclusively, unless given special dispensation or it's a co-promotion) for set terms, either a length of time or a number of fights. They can be sued for breaching contract, which has actually happened many times.