This is a boxing mobile game on iPhone and Android. Don't let the 8-bit graphics fool you, this is a fairly deep boxing game with an impressive career mode and controls perfect for your mobile. You create your boxer, decide what type of boxer he's going to be, then go about training and scheduling fights.
The calendar moves in a weekly format, and you can choose what your fighter does each week. You can also spectate other fights on the card, and also choose whether to play your fight or just spectate (at which point your boxer fights according to the tendencies you've assigned it). The career mode so far I'm finding is deep and worth digging around in. As for the fights, I'm enjoying that as well-the controls are simple and easy to pick up. Only played a few fights but I'm also noticing the opponents will fight according to what they are (brawlers brawl, out boxers will try to keep their distance, counter punchers attempt to pounce on your misses, etc.).
This game is free to download on iPhone, with an option to buy the Premium version which unlocks full league customization as well as a Promoter mode where you book the fights and can even manage online leagues.
This is worth checking out.