Although American mythology has held that "every child has a chance to go to Harvard," a relative handful of secondary schools continue to serve as the funnel to the nation's most selective private colleges and universities.

The Horatio Alger dream, admissions officers say, has been brought nearer to reality in the last two decades with expanded recruitment and financial aid programs.

Nevertheless, they acknowledge that a few hundred private, parochial and affluent public schools still provide the bulk of their students year after year.

"The block you're born in still tends to dictate your educational experience," said Fred Hargadon, director of Stanford University's undergraduate admissions and chairman of the College Board.

Private preparatory schools provided 24 percent of last year's freshmen class at the nation's most selective colleges, and parochial schools supplied another 7 percent, according to a survey by the University of California in Los Angeles.

UCLA defines "most selective" as private colleges and universities in which the students' combined math and verbal scholastic aptitude test scores average 1.175 or above.

For public universities the average must be at least 1,100. By this definition, some 98 colleges or universities out of the nearly 3,000 in the country qualify. They include such institutions as Union in New York State, Grinnell in Iowa and Bowdoin in Maine, along with traditionally competitive ones such as Harvard, Stanford, Brandeis, California Institute of Technology and Amherst.

In the 1960s, the percentage of public school students at these highly competitive institutions increased as national enrollment in public schools grew by 9 million. But admissions officers say the balance has held constant in the 1970s and in some cases has swung the other way.

At the same time, admissions officers say that, in the public sector, there is a predominance of students from a limited number of high schools serving what The Wall Street Journal has called "the new class" -- the families of the upwardly mobile and affluent managers and professional people who have "made it" since World War II.

Yal's admissions director, Worth David, says that most of the public high schools that consistently supply students are in "managerial, professional communities where the parents tend to demand advanced work. Ther's a clustering around these schools."

Brown's admissions director, James H. Rogers, estimates that "60, maybe 100 public schools are supplying most of the applicants to the most selective schools."

"They all have one thing in common -- damn high tax rates," he added. "These schools draw people who can pay the taxes."

In interviews with eight admissions directors from coast to coast recently, the same high schools were mentioned repeatedly: New Trier in Winnetka, Ill.; Beverly Hills, near Los Angeles; Walt Whitman in Bethesda, Md.; Shaker Heights near Cleveland; Shawnee mission near Kansas City and a few others in affluent suburbs.

Also mentioned as significant sources of applicants were a few selective academic high schools in big cities, such as Bronx High School of Science in New York and Boston Latin.

Educators hasten to warn against drawing sweeping conclusions from these facts.

They note, for example, that attendence at a selective, highly competitive private, university is no guarantee of success in later life.

They also note that excellent public universities, and some private ones, provide abundant additional avenues.

The most selective institutions enrolled only a small percentage of last year's 1.7 million freshmen, 86 percent of whom came from public schools. Iowa State, ranked as one of the most selective public universities, draws only 7 percent of of its students from nonpublic schools, and at the private California Institute of Technology, which has the highest average test scores in the nation, the private-school figure is 17.5.

Nevertheless, the most selective institutions still turn out a disproportionate share of the nation's managers, bankers, lawyers, politicians and opinion makers. And economic and family background still appear to be major factors in getting into the pipeline, despite extensive efforts by these colleges and universities to broaden their enrollment base.

In the late 1950s, Harvard led the way in recruiting applicants from more high schools. Today, it has 2,800 alumni across the country interviewing candidates and scouring local communities.

Other Ivy League colleges followed suit. In the 1960s, Yale President Kingman Brewster clashed with alumni over his policy of expanding equality of opportunity for admission.

These policies have had results, admissions officers say. For example, the 2,128 students admitted to Yale last spring came from 900 schools, twice the number as in the mid-1950s.

Yet even that larger, more recent number represents only 5 percent of the roughly 18,000 high schools in the nation.

"In every study I've ever seen, where you're born and how you're born has a great deal to do with how you're going to be educated," said Brown's Rogers. "We don't like this. Nevertheless, it's the case."

When Horace Mann outlined plans for a vast public education system earlier in the nation's history, he envisioned that public education would be "the balance wheel of the social machinery."

But educators now agree that this process of equalizing through education has worked more slowly than Mann expected.

The UCLA survey of the most selective private colleges and universities estimates that about 45 percent of the students are from families earning more than $40,000 a year, and 10 percent are from ones earning more than $100,000.

(By UCLA's definition of average test scores, the "most-selective" list includes such institutions as Duke, Rice, Tulane, Brandeis, Colgate, Dickinson and Bates as well as Ivy League institutions as Brown, Yale, Princeton and Harvard.)

Perhaps not surprisingly, the schools that stand out dramatically in the 1980 list of National Merit Scholarship semifinalists also show a correlation with income and family background.

For example, Los Alamos, N.M., high school, which serves a city of $20,000, almost all of whom are associated with the federal nuclear laboratory, had 30 National Merit semifinalists. This was one-third of all the semifinalists in the state.

In the District of Columbia, there were 54 semifinalists, of which 49 came from private or parochial schools. A single school, Woodrow Wilson, provided all the District's public school semifinalists.

In the Maryland suburbs, Bethesda had a total of 58 semi-finalists, compared with 18 in Prince George's County.

Similar pockets of high performance exist around the country.

And although test scores are not the only factor that selective institutions consider in admissions, they are an important one.

Brown's Rogers says that his university is looking for diversity. In the 1980 competition for a place at Brown, applications from 11,180 students at 3,129 schools were considered. But, as in years past, a small number of schools predominated in the final cut to 2,000.

Landover, a private boarding school in Massachusetts, received 40 acceptances. And some 20 public high schools which sent in 50 or more applications, also did well, Rogers said.

The continued strong showing of private and parochial schools in the stiff competition for places in the highly selective institutions, college admissions experts say, is the result of a number of factors.

Most important is the fact that private schools have become far more selective than they were in earlier days, when prep schools primarily were for rich children and the recalcitrant.

Union college's new freshmen class will be 20 per cent from private schools, up from 15 percent the previous year. "I want this up to 35 percent," says admissions Dean Kenneth A. Nourse. "Private schools are chock full [of candidates]. There are lines of parents at the front doors of those schools, which tells you something about public education."

Last year, Phillips Exeter Academy, a private school in New Hampshire, had the second most national merit semifinalists (45) in the country after Stuyvesant, a public high school in New Ork City, which had 48.

Also, parochial schools, and well-endowed private schools which recruited minorities in the 1960s and 1970s have become a source for colleges which also are seeking more minority applicants.

Harvard's admissions director, William Fitzsimmon, said that at least a third of minority admissions are from parochial or private schools. This is about the same ratio as for this fall's entering class of freshmen.

"On the average, private schools provide better preparation, a higher level of parental education and 'push,'" he said. This could account in part for the fact that private school students make up only a quarter of Harvard's applicants but account for a third of those admitted.

"I'm a great advocate of public education," he said. "But the private schools set the pace and their quality is good for everybody. They are elitist -- in the academic sense. But that's healthy."