Teresa Sullivan speaks at a Bloomberg Innovation and Economy roundtable event in Washington in October. (Andrew Harrer/BLOOMBERG)

The board’s roster includes the son of a televangelist, the president of the largest beer distributor in Houston and the 166th wealthiest American. There are doctors, lawyers and, of course, alumni.

And most of the 16 voting members of the University of Virginia’s governing board of visitors have given campaign contributions to governors who appointed them. In some cases, donations added up to hundreds of thousands of dollars.

The board has drawn intense scrutiny this week after it ousted U-Va.’s popular president, Teresa Sullivan, with barely a word of warning to state lawmakers, the university community or Sullivan herself.

The campus erupted in protest at the board’s decision to remove Sullivan after less than two years, one apparently made in quiet conversations over several months. Faculty, staff and alumni are demanding explanations. But board members have said little. This week, they have referred calls and e-mails to the board’s leader, rector Helen E. Dragas. On Tuesday, two days after the ouster of Sullivan was made public, Dragas did not respond to a request for comment.

There are about 200 seats on boards overseeing state universities, which are among the most coveted appointments a Virginia governor can offer. The board at U-Va. — a premier public university — is the top prize.

Seats typically go to supporters, donors, friends and those who are owed a favor.

But Gary C. Byler, a Republican activist appointed to the board of Christopher Newport University last year, said sometimes it’s more than that.

“It isn’t just cash contributions,’’ he said. “It’s more of an issue of philosophical agreement.’’

Gov. Robert F. McDonnell (R) said last week in an interview that he looks for those who share his goals of reducing college costs, increasing slots for in-state students and making schools more efficient. He said he regularly receives input from presidents, other board members and a group charged with making recommendations.

“If you’re going to have a new vision for higher education and you’re going to have new major reforms that you want to put in place, you need new managers to carry out that vision,’’ McDonnell said.

Boards wield enormous power hiring and firing the president, setting tuition rates, managing finances and approving faculty tenure.

Members, who can serve up to two four-year terms, are not paid.

Former governor L. Douglas Wilder (D) said political considerations play a part in selecting board members. “There’s no need to duck that,’’ he said.

But Wilder said he also tried to judge what the potential member could offer besides being a graduate. Could they bring in grants? Could they help recruit a diverse student body? Could they raise money?

“The autonomy of schools is always to be respected, but the governor does have the responsibility to shape them,’’ he said.

U-Va.’s board is split equally between members appointed by McDonnell and former governor Timothy M. Kaine (D). Kaine, now the Democratic candidate for U.S. Senate, declined to comment Tuesday.

McDonnell will appoint another group of board members at the end of this month, including four at U-Va. Two members at U-Va. are term-limited, but the other two could stay on for another four years.

Kaine appointed Dragas to the board in 2008. A Virginia Beach developer who received two degrees from U-Va., Dragas has contributed nearly $20,000 to candidates since 2002, including $6,000 to Kaine, according to the Virginia Public Access Project, a nonpartisan tracker of money in politics.

Other U-Va. appointees include a former Democratic legislator; a partner at the prominent Richmond law firm McGuireWoods; and the heads of financial, wireless and energy companies.

Kaine appointed R.J. Kirk, a Radford resident who founded a pharmaceutical company, who was the 166th-wealthiest American in 2011, according to Forbes. He has contributed more than $2 million to candidates since 1999, including $785,000 to Kaine and $300,000 to McDonnell, according to VPAP.

McDonnell’s appointees include John L. Nau III, president of the largest beer distributor in Houston, who has donated $189,000 to candidates, including $65,000 to McDonnell; and Tim Robertson, son of televangelist Pat Robertson, who leads an investment holding company and has contributed about $45,000 to McDonnell.

Among academics in Charlottesville, the board is regarded as a relatively conservative and pro-business group. There are no educators on the panel.

The board does have a nonvoting student, Hillary Hurd. On Tuesday, the Cavalier Daily student newspaper quoted Hurd as saying that the board’s decision on Sullivan “will prove in time to have been a wise one.”

Many board members across the state are in regular contact with McDonnell — some individually but more often on conference calls or receptions at the governor’s mansion. The governor has taken a hands-on approach with the schools, but primarily on tuition and finances.

“My goal is to appoint excellent board members,’’ McDonnell said in the interview. “I leave the governance of the universities up to them — from hiring the presidents and faculty to setting tuition rates.”

Researcher Magda Jean-Louis contributed to this report.