The city says more families than usual are applying for pre-k seats in public schools. So far, 21,700 applications have come in, a 27 percent increase over the same time last year.

Sophia Pappas, Executive Director for Department of Education's Office of Early Childhood Education, attributes the increase to Mayor Bill de Blasio's plan to provide universal, full-day prekindergarten.

"I would say it's all the excitement and momentum around getting more full-day pre-K in the city," she said.

The application numbers are just for public schools, not pre-k programs at community-based organizations. The city is currently reviewing proposals from schools and community organizations seeking to expand the number of children they can serve for a full day. Many currently only provide half-day programs, which are not considered sufficient for working families.

Last month, the city announced that it had received proposals for 29,000 more seats from both public schools and community-based organizations, which is more than the 21,000 it is seeking by September. This would bring the total number of full-day seats to 53,000, a significant increase.

But even if the city gets the money it's seeking from Albany, it has limited space in its public schools. It currently provides about 16,000 full-day seats, and is seeking to add another 4,200. So the demand is already well above the supply. The city has no breakdown yet for which neighborhoods have provided the most applications, or whether they will have more seats. All of this matchmaking will need to happen swiftly if the funds materialize by Albany's April 1 budget deadline.

Pappas said her staff is presuming the money will come through, so the DOE is now reviewing proposals from individual schools to expand their programs and will know by the first week in April which schools will get how many extra seats. The application deadline was extended until April 23.

That gives families just a few weeks to adjust their applications, and some parent leaders worry this will be a tight squeeze.

Tesa Wilson, president of the Community Education Council for District 14 in Brooklyn, said many parents still have questions, even after attending D.O.E. information sessions.

"There's still so much confusion about where seats are going to be," she said. Furthermore, she said many parents aren't comfortable about enrolling their children in public school pre-k programs without having a guarantee that their child can attend kindergarten or first grade in the same school.

The city is planning to tell community-based organizations in May and June whether they will be able to expand, giving families more options if they don't get space in public schools. The vast majority of the additional seats will be in community-based organizations.

Steven Antonelli, administrative director of Bank Street Head Start in the East Village, said he's sure interest in free pre-k programs is growing because private programs can be very expensive.

"I think it raises the consciousness of parents in general, and they realize that there is another option," he said. "I think also the community-based organizations are sort of beating the bushes too because they want to fill their UPK contracts."

Even if the city does get new pre-k funds from the state, other hurdles remain. It will have just a few months to get the classrooms organized and hire teachers. Pappas said the D.O.E. will expand outreach efforts and summer training.