The digital age may claim another victim.

The residential White Pages, those inches-thick tomes of fine-print telephone listings that may be most useful as doorstops, could stop landing with a thud on doorsteps across New York later this year.

Verizon, the dominant local phone company in the state, asked regulators on Friday to allow it to end the annual delivery of millions of White Pages to all of its customers in New York. The company estimates that it would save nearly 5,000 tons of paper by ending the automatic distribution of the books.

Only about one of every nine households uses the hard-copy listings anymore, according to Verizon, which cited a 2008 Gallup survey. Most have switched to looking up numbers online or calling directory assistance. The phone book for many people, it seems, has gone from indispensable tool to unavoidable nuisance.

“Phone books have been a very visceral issue,” said Scott Cassel, executive director of the Product Stewardship Institute, an environmental group in Boston. “They do tend to pile up, particularly in apartments. More and more, people are finding that they don’t need them, but they can’t find a way to make them stop.”