George Mason University unveiled yesterday what its president, George Johnson, acknowledged was "a huge asking list" of building projects for Virginia's fastest-growing university.

In a presentation to Gov. Gerald L. Baliles and legislative leaders, Johnson noted that "it is not realistic" to think that the state will finance all of the $53 million in requested projects in the next budget cycle, but it didn't stop him from trying.

Johnson asked Baliles and members of the General Assembly's money committees to help him solve "a dilemma" resulting from the school's growing size and reputation.

"I can't realistically ask you to help us catch up {with building needs in the next biennial budget}, but if I don't, I become part of the problem," Johnson said at a luncheon meeting at the school's Metro campus in Arlington.

The governor and about 30 key legislators and Cabinet secretaries stopped at GMU during the second day of a four-day tour of state facilities, an every-other-year ritual that is a key component in deciding what capital projects are funded.

Aware that the legislators who slice the budget pie are more likely to have ties to the state's older schools, Johnson emphasized that GMU, which opened in 1957 as a two-year college with 17 students and now enrolls 17,900, does not seek to compete with other institutions, but is carving its own niche.

Nonetheless, he said, it is essential that Mason "rival in quality" three state schools it views as its academic peers: the University of Virginia, the College of William and Mary, and Virginia Tech.

Johnson dazzled his visitors with computer-enhanced charts and graphs that he said illustrated that GMU lags far behind those schools, and the state's two other doctoral-granting institutions (Virginia Commonwealth in Richmond and Old Dominion in Norfolk), in physical facilities and faculty-student ratio.

For example, he said, GMU has 40 square feet of space for each full-time student, compared with 110 at U-Va., 95 at William and Mary, 86 at Tech, 75 at Virginia Commonwealth and 65 at Old Dominion.

Mason is now the state's third-largest school, behind only Tech (22,000 students) and VCU (19,000). Before the end of the century, it will be No. 1, Johnson said.

To deal with its growing pains in the short term, Johnson said GMU needs 210 new instructors in the next two years and an additional 400,000 square feet of space.

Mason's $53 million expansion plan comprises 19 requests, headed by $11.4 million for a second science and technology building and $10 million for a library addition at its main campus south of Fairfax City, and must compete with similar requests from the state's 14 other four-year colleges.

Together with proposals from the state's two dozen community colleges, a total of 279 education projects, costing $700 million, are being requested for inclusion in the 1988-90 budget that the legislature will consider in January.

The governor and legislators consider the schools' stated priorities and recommendations from the State Council of Higher Education, which ranked projects in seven groups.

Mason's proposed library addition and $500,000 for renovation of Krug Hall fared well with the council, appearing in the second group, but the science building, which Mason placed first on its list, is in the council's bottom category.

Such a low ranking makes financing for the building highly improbable next year, legislators said.

Also rating a spot in the council's second group is a request for $5.5 million to expand the Woodbridge campus of Northern Virginia Community College, which, with 33,000 students at five campuses, has passed Miami-Dade as the nation's largest community college.