Sure there is; the rules for decertifying unions and replacing them are not mysterious.
> They somehow got in control of union representation for the entire UC system.
Because the grad students formed unions and voted to affiliate with UAW, even before their rights to do so were recognized.
> I’m not familiar enough with labor law to know the exact proceedue, but presumably students would need to mount a state-wide campaign to vote UAW out (if it is even possible).
That's the main option (they'd need support of 30% of the represented employees to force a vote)
In principle, they could also challenge the designation of a single statewide bargaining unit and argue that the separate campuses (or at least, their campus) grad student workers are somehow not part of a community of common interest with the rest of the existing BU, which would allow separate decertification for just their campus.
But why? They’ve got nothing to do with the car industry.
UAW provided organizing and other support beginning shortly after the first few (unrecognized) campus unions were set up by the grad students.
Wow, and there are people arguing that free market will solve it!
The US is a closed shop country, so it is illegal for students to simply cancel their membership in UAW and join a graduate student workers union.
I’m not familiar enough with labor law to know the exact proceedue, but presumably students would need to mount a state-wide campaign to vote UAW out (if it is even possible).
Even then, I don’t know if campuses would be allowed to negotiate separately or not.