A new study of admissions at 30 highly selective colleges found that legacy applicants get a big advantage over those with no family connections to the institution  but the benefit is far greater for those with a parent who earned an undergraduate degree at the college than for those with other family connections.

According to the study, by Michael Hurwitz, a doctoral student at the Harvard Graduate School of Education, applicants to a parent’s alma mater had, on average, seven times the odds of admission of nonlegacy applicants. Those whose parents did graduate work there or who had a grandparent, sibling, uncle or aunt who attended the college were, by comparison, only twice as likely to be admitted.

Legacy admissions have become an increasingly touchy issue for colleges. Admissions officers mostly play down the impact of legacy status. But a growing body of research shows that family connections count for a lot  and Mr. Hurwitz’s study found a larger impact than previous studies.

And at a time when admission to elite colleges has become increasingly competitive, critics say the legacy admissions advantage stands as an undemocratic obstacle to social mobility.