The group that tests 4- and 5-year-olds applying to private kindergartens is reporting a jump in New York City-based test-takers, providing statistical confirmation for claims by parents and admissions officers that this was a particularly competitive year for private school admissions.

The number of children who took the test this year was 3,100, a 15% jump from last year, when 2,700 students took the tests, given by the Educational Records Bureau and known by the acronym ERB. The number of spots in private kindergartens is around 2,400, according to the Independent School Admission Association of Greater New York.

The figure matches reports that elite private schools this year received record numbers of applications, with schools from standard top choices to a newcomer, the Claremont Preparatory School in Lower Manhattan, receiving more applications than ever before.

During the admission season that ran from October to February, observers puzzled over whether the flood of applications meant more children were applying or whether the same number of parents, more frightened than ever about being rejected, were now sending out more applications per child.

The head of Grace Church School in Greenwich Village, George Davison, said the ERB figures provide an answer to the chicken-egg puzzle. “There are more 4- and 5-year-olds in New York City who want to attend independent schools than there were before, by a substantial margin, and that’s where the increase in applications came from,” Mr. Davison said.

Schools across the city have been reporting a record number of applicants to their kindergarten and prekindergarten programs.

This year, Grace Church School admitted 29 4-year-olds out of 220 who applied, a 13% ratio. Trevor Day School on the Upper East Side accepted less than 9% of its 450 applicants, only 40 4-year-olds.

Even a school considered an easy bet by many parents because it has only been open for two years and had many extra spots, Claremont Preparatory in Lower Manhattan, created a waiting list for the first time ever, the admissions director, Dana Haddad, told The New York Sun.

Another coveted program that is publicly funded, Hunter College Elementary School, likely dealt out the most heartbreak, with a record 1,550 4-year-olds applying for just 48 spots, meaning the school has space for less than 5% of applicants, its director of admissions, Lindley Uehling, said. Ms. Uehling estimated she received about 300 more applications this year than last year.

While the crunch is prompting some parents to discuss moving to the suburbs, other families have been pushed into public schools.

Two blond-haired brothers who played outside P.S. 234 in TriBeCa yesterday are at long last transferring to the Saint Ann’s School in Brooklyn this September, their nanny said. The boys’ parents tried to get them into Saint Ann’s last year but could not find seats — even though their father is an alumnus of the school, said the nanny, who asked not to be named.

She said the boys’ parents tried again at Saint Ann’s this year, because of their experience at P.S. 234, which is brimming with students.

Indeed, public schools in affluent neighborhoods are feeling the effects of the city’s baby boom.

A Battery Park City mother, Blake Vaknin, with two children at P.S. 89 in TriBeCa said she has watched enrollment grow since her daughter started kindergarten two years ago. At the time, an initial plan to have two kindergarten classrooms had to be expanded to three.

When her son entered kindergarten the next year, three classes were expanded to four — and the fourth, her son’s class, was held on the third floor in what used to be the art room.

Her son hiked up the three flights of stairs to class. Her next worry is her 2-year-old daughter, who comes along with her every day to pick up the older children at dismissal time.

She would like her youngest daughter to follow her siblings into P.S. 89. But she said she worries that, with more residential buildings coming and few new schools, there might be no room.

“You live in a nicer neighborhood, you expect to have certain amenities,” Ms. Vaknin said.

A mother at P.S. 234, Dawn Cook, said the rising ERB numbers could reflect panic among public school parents. “People are getting frightened that there’s not enough space in public schools,” Ms. Cook said yesterday, as she stood with a pack of parents lining the Greenwich Street school waiting for her three children to be dismissed.

One mother standing next to her was Jane Pratt, the creator of Jane magazine, who has a daughter in kindergarten at P.S. 234.

Ms. Pratt, who said she moved to TriBeCa about six months ago, appeared momentarily unsettled by the talk of crowding, which has led schools including P.S. 234 to create waiting lists for families who live in the neighborhood but cannot be accommodated.

“If they’re already in, they’re okay for next year, right?” she asked Ms. Cook.

Ms. Cook responded with a reassuring “yes.”

Ms. Pratt said she does not expect the kindergarten boom to abate anytime soon.

“Everyone I see in this area is either pushing a stroller, a single stroller, or a double stroller — and they’re pregnant,” she said.