Okay heres the answer. You guys have to realize that basketball is actually a more popular sport than football due in large part to the tournament. You said "largest fanbases" and that means bandwagon jumpers primarily.
1. Texas
2. Kansas
3. Oklahoma
4. Nebraska
5. Missouri
6. Colorado
7. Texas A&M
8. Oklahoma State
9. Kansas State
10. Iowa State
11. Texas Tech
12. Baylor
PCR is correct -- those are the four teams from the big XII that sell merchandise nation-wide and have the name recognition to draw TV ratings (ku, nu only in specific sports). The other big XII programs are basically inconsequential to the rest of the nation. It's no coincidence that those are the only teams that have won (or been close to) multiple national championships and are still viable within at least one sport (NU running entirely on tradition by now). There is a very significant bandwagon following of those four teams, proportionate to season and how well each is doing in a particular year.
You can decide if you want to count people as "fans" who will turn on a game when these teams are playing, and even buy merchandise, but never attended a game at the school.
imo, a true "fanbase" is better defined as the people who directly support the athletic department -- donors, ticket holders, travel to away games, etc...