College athletes mounted their latest and strongest charge against the idea that they are amateurs as they began a court challenge on Tuesday of the NCAA’s power to limit their compensation in a multibillion-dollar industry.

Former athletes in Division I men’s and women’s basketball and top-division football are seeking to end the NCAA’s cap on what they may receive for participating in college sports: generally, little more than tuition, room and board.

The plaintiffs in “In Re: National Collegiate Athletic Association Athletic Grant-in-Aid Cap Antitrust Litigation” say the NCAA’s rules violate U.S. antitrust laws by artificially depressing athletes’ compensation. Previous litigation by athletes sought to stop the NCAA from profiting from their name, image or likeness without sharing the proceeds, but in this case they’re seeking to change the basic relationship between college sports leaders and participants.

The NCAA says compensation limits are necessary to maintain the distinction between college and professional sports, and that letting schools pay athletes unlimited sums would erode college sports’ appeal to the public. NCAA officials say athletic scholarships and the chance to earn a college degree—in many cases worth a few hundred thousand dollars—are ample compensation for what they say is an amateur pursuit.

“What sets college sports apart is that the competitors are students and not paid professionals,” NCAA lawyers wrote in their prepared opening remarks, released ahead of Tuesday’s trial start. They warn that a “competition between athletes recruited and paid based on the value of their performance, on one hand, and athletes who compete just as part of their student experience and a way to maintain it, would readily degenerate into an uninteresting and potentially dangerous mismatch.”