Last season Big12 games were broadcast on ABC, FOX, ESPN, ESPN2, ESPN+, FS1, and FS2 (although there were only 2 games that showed up on FS2 and they both involved Texas Tech).
Technically games could be on ESPNU or ESPNNEWS, but I assume that any game not on ESPN or ESPN2 would just get shown on ESPN+.
Out-of-conference games on the road can certainly end up on other networks. BYU and Utah each have a game on CBSSN. Other Big12 teams are scheduled (so far) to play OOC games on CBS, NBC, SECN, and ESPNU.
It will be interesting to see how games are scheduled throughout the year with no UT or OU in this conference.