Digital books are the fastest growing area of publishing, and libraries are seeing a surge in demand for e-book titles — but finding an e-book can be tough.

The Central Library in Queens became the first in New York City to start lending e-readers last month — 50 of them, pre-loaded with dozens of books each.

“They went as quick as the customers came through the door, the e-readers was gone,” librarian Wanda Wright said.

The e-reader program is primarily for users who don’t already have devices or can’t afford them. For those who do, the library offers thousands of e-books patrons can download on their own.

“In Queens we have over 70,000 books a day that we check back in and 70,000 going out. So in a digital world, there’s considerable savings for libraries,” said Queens Library CEO Tom Galante.

As libraries struggle with years of successive budget cuts, the new medium could bring some relief because it eliminates the cost of labeling, shelving and tracking books. But finding an e-book can be tough.

Most of the major publishers refuse to allow libraries to lend their titles. Others impose restrictions or charge double or triple the print price.

The American Library Association reports that the e-book “Eisenhower in War and Peace,” costs more than $100 a copy. Amazon sells it retail for $20.

Beyond availability, there’s another problem: Almost all U.S. libraries that offer e-books do so through an outside company called Overdrive, which does not give libraries ownership of the content.

“Every year you have to pay them to continue to use that subscription service or you lose the content you’ve already paid for,” Galante said.

The rate is negotiated from library to library.

If a library stops using Overdrive, they could lose all the books they’ve licensed through them.

For the first time, libraries are renters, not owners, of their content. And, the more e-books they purchase, the larger the problem becomes.

Robert Wolven heads an American Library Association group that’s trying to figure out what a new model would look like and how to create it…one that all publishers can buy into, without a middle man.

“These are questions that go beyond what we’re doing now and what we’re doing next year,” Wolven said. “We’ve talked about how we want to avoid developing the model for next year that’s going to be obsolete by the time anyone puts it in place, and that’s a real challenge. “