Originally founded by Professor James Buchanan (the guru of the 'Public Choice' ideology) and run by Economics Professor Robert D. Tollison (with some help from Richard E Wagner) It was originally housed at Virginia Polytechnic Institute and State University, but then transferred, along with Tollison, Buchanan and a number of 'Public Choice' academic enthusiasts, to the corporate-funded George Mason University.
It was used at GMU by Tollison to run his Cash for Comments Economists Network along with James Savarese. He paid Carol M Robert and Elizabeth Masaitis from the Center to provide editorial and organisational work for his Tobacco Institute-funded network of economists. Anne Tollison was also employed by the Center for a while to supervise this operation.
Don't confuse it with the Center for the Study of Popular Choice -- or with the North Dakota Center for Study of Public Choice and Private Enterprise (Director Jeremy Jackson in 2016)
Cash for Comments Economists Network
Robert D Tollison and Anne Tollison
Carol M Robert and Elizabeth A Masaitis
Public Choice is not so much an economic theory as it is a an extreme form of libertarian small-government, low-or-no-regulation ideology. The practitioners therefore had no ethical or moral qualms about taking tobacco industry money to help promote a "legal product". So Tollison's think-tank acted both as an academic association and as a vehicle for lobbying on behalf of the tobacco industry.
Those attracted to this free-market, low regulation, form of economics are -- by definition -- academics who have no problem with usurping the reputation of a university and converting it to a propaganda vehicle for the preservation of the right to smoke ... provided they got paid hansomely for their efforts. See this explanation of 'Public Choice' economics from an encyclopedia of economic theory:
Public choice takes the same principles that economists use to analyze people's actions in the marketplace and applies them to people's actions in collective decision making. Economists who study behavior in the private marketplace assume that people are motivated mainly by self-interest. Although most people base some of their actions on their concern for others, the dominant motive in people's actions in the marketplace—whether they are employers, employees, or consumers—is a concern for themselves.
See this fairly clear and rational explanation  and the more esoteric theoretical explanation: 
Professor James Buchanan was the founding guru of the Center for Study of Public Choice when it was at the Virginia Polytechnic Institute. It later moved to George Mason University when Buchanan led the Polytechnic's Economics Department in a walk-out. They transferred as a group to the new corporate-funded George Mason University which not only tolerated personal greed, but made this the university motto. At that time Buchanan, Tollison and Richard E Wagner were disciple of Friedrich Hayek and the all had links to the American Enterprise Institute - controlled at that time by William Baroody and Irving Kristol, and funded (as was GMU) by the larger manufacturer of consumer products. Later they developed even stronger links to the Independent Institute.
1 Sportometrics - the height of absurdity
2 Recent Transitions
3 George Mason University
Sportometrics - the height of absurdity
In 1985 Robert Tollison, Richard Higgins of the FTC, and Brian Goff completed a paper on "economic research into the play and institutions of sports" at the CSPC. They used Public Choice theory to...:
explained the process by which runners decide to supply effort during a race ...
demonstrated empirically that professional basketball players who competed in states with open high school basketball competitions survive longer in the National Basketball Association.
[They explained that] "Sportometrics," or the use of sports and sports data to test economic hypotheses, will continue to be of interest to some Center Scholars over the next several years.
There are conflicting data about the recent changes to the Center. The Mercatus Center (Who's site is also at GMU) says:
The Center moved to George Mason University in 1980, where it merged with the Center for the Study of Public Choice during 1998 to become the James M. Buchanan Center for Political Economy. The Mercatus Center writes of the move that "Once again, support from the Charles G. Koch Charitable Foundation provided the critical funding for this formative move." The Mercatus Center brand was developed in 1999 from the James Buchanan Center.
However the tobacco archives (recording documents in 2001) don't register the Buchanan Center, but continue to show funding of Mercatus and CSPC.
In 2016 the CSPC was being run at George Mason University by Dr Alex Tabarrok.  who doesn't figure in a significant way in any of the tobacco archive documents -- except, as an index entry for "The Perils of Setting a Constitutional Order", Foreword to Penelope Brook Cowen, Tyler Cowen & Alexander Tabarrok, "An Analysis of Proposals for Constitutional Change in New Zealand (1992).
Robert Tollison died in October 2016. His obit by Peter Boettke, reveals links to the think-tank Citizens for a Sound Economy. 
George Mason University
The 1985 Annual Report of the CSPC says about its relationship with GMU:
The Center for Study of Public Choice is an integral part of George Mason University. While maintaining its separate identity, the Center staff is part of the George Mason Economics Department. As such, the university budget covers the salaries of the permanent Center staff and minimal operating expenditures. Excluding the physical facility which houses the Center, St. George's Hall, general university support in 1984 additionally amounted to some $500,000 on an annual basis.
Center activities extend beyond those supported by the university. Funds for summer and release-time research, guest lecturers, visiting scholars, graduate students, and for supplemental travel and operating expenses have been provided by external supporters. External support in 1985 summed to approximately $300,000. These funds were provided by numerous external supporters, to whom we are very grateful for their sustained support over the years
George Mason Uni was founded in 1972 on a campus just outside Washington DC. It is now Virginia's largest public research university with 34,000 students on campus, ten schools and colleges, It no longer advertises it CSPU, however it does still have a Mercatus Center which was a research-based center used by the tobacco industry 
All Google entries which are indexes under the terms "Tollison" AND "Mercatus" seem to be expunged.
In April 2016, GMU renamed its law school the Antionin Scalia School of Law after receiving a $10 million gift from the Charles Koch Foundation and another $20 million from an anonymous donor which was funnelled through Leonard Leo, the executive VP of the Federalist Society. Between 2011 and 2014 the Koch's gave $48 million in donations to the GMU according to the Associated Press - and it is this money which supports the free-market Mercatus Center. The Mercatus board includes Richard Fink (Exec VP of Koch Industries, and Charles Koch himself.
Charles Koch also chairs the board of the Institute for Humane Studies at GMU.
The Mercatus Center is also linked to the National Federation of Independent Business and the American Legislative Exchange Council (ALEC). Source: Sourcewatch.orgmore » « less
|Public Choice Society||Gordon Tullock, Edward J. Lopez, James McGill Buchanan|
|Cato Institute||Tyler Cowen, James McGill Buchanan|
|Federal Trade Commission||James Clifford Miller III|
|Office of Management and Budget||James Clifford Miller III|
|US Postal Service||James Clifford Miller III|
|American Enterprise Institute||James Clifford Miller III|
|George Mason University||Tyler Cowen|
|Council for National Policy||James Clifford Miller III|
|Americans for Prosperity Foundation||James Clifford Miller III|
|Office of Information and Regulatory Affairs||James Clifford Miller III|
|Progress and Freedom Foundation||James Clifford Miller III|
|Sound Economy Foundation||James Clifford Miller III|
|Mercatus Center||Tyler Cowen|
|Clean Energy Fuels Corporation||James Clifford Miller III|
|The Independent Institute||Edward J. Lopez|
|Americans for Prosperity||James Clifford Miller III|