Warner filed a trademark transfer for the Rush games back when they bought most of Midway so it's a good guess they own it. Then again it turns out Microsoft bought Hydro Thunder so who really knows.
Yeah my understanding is that:
EA wound up with NBA Jam (not sure if that includes Hangtime or Showtime) and NFL Blitz (I assume that doesn't include Blitz: The League)
MS (tragically) wound up with Hydro Thunder
And Warner got everything else. I think a big part of what makes who owns what confusing is that you'd think Warner would leverage the fact that they own most of Midway's library of games by re-releasing a lot of those classic games in some way or by making new games based on those properties but they've done very little of that.
They put out a compilation of games on 360 and PS3 that was fine but if you owned Midway Arcade Treasures vol 1 then you didn't really have a reason to buy it and then they put out an MK compilation that was somehow worse than the Midway Arcade Treasure versions of those games and that's it. Oh and they put out that Midway Lego Dimensions pack which is cool but requires a $100 game to play it.