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The abandoned ashes are stacked floor to ceiling in the basement of the Graham, Putnam and Mahoney Funeral Parlors, tucked neatly on wooden shelves and tables and in an unused dumbwaiter.

Someone loved the people once, enough to have their bodies cremated — then promptly forgot or decided they didn't want them.

"The fact is, if no one claims them, there's nothing you can do with them," said funeral director Peter Stefan, of Worcester. "You can't throw them away. They could be Uncle Freddy's ashes. They could come and sue you."

Storage or disposal of abandoned ashes is a growing national problem, as the number of cremations is on the rise. Even in states that allow the burial or scattering of abandoned ashes, some funeral homes store them for years, hoping one day to place them in the hands of a relative.

A majority of states have laws setting minimum waiting periods for funeral homes to store unclaimed cremated remains, ranging from 60 days to four years. About a dozen states have no laws or regulations. A handful, like Massachusetts, just have regulations.

Massachusetts' regulations require funeral directors to contact next of kin and hold remains for six months. If the ashes remain unclaimed, the funeral home must contact the family by certified mail and wait another 60 days before disposing of the ashes.

Funeral directors worry the regulations don't carry the protections of a law, so they have been holding on to the ashes — just in case.

They've succeeded in getting a bill to Gov. Deval Patrick's desk requiring funeral homes hold unclaimed ashes for 12 months — after which they could be buried in a common grave, crypt or scattered in a cemetery.

The bill requires funeral homes to keep permanent records of the remains and frees them of legal liability. An aide for Patrick said he's reviewing the legislation.

David Walkinshaw, spokesman for Massachusetts Funeral Directors Association, said the vast majority of funeral homes in the state, including his own, have unclaimed remains.

"There needs to be a dignified way to finally put these people to rest and allow the funeral homes to do that under the law," said Walkinshaw, who has ashes dating back 30 to 40 years.

In 1975, just 6 percent of deaths in the United States resulted in cremations. By 2006, the number had grown to nearly 34 percent, according to the Cremation Association of North America. That could increase to more than half of all deaths by 2025.

The popularity of cremations varies greatly by state, from less than 10 percent of all deaths in Alabama and Mississippi to more than 60 percent in Hawaii, Nevada, Washington and Oregon. In Massachusetts, about 30 percent of those who die are cremated.

Unfortunately, some families may not realize that cremation isn't the end of the process, according to Dennis Werner, a member of the Cremation Association board and general manager of St. Michael's Cemetery and Crematory in the New York City borough of Queens.

"You'll hear people say all the time, 'Just cremate me and throw me in the river,"' Werner said. "The more the word gets out that cremation is not final disposition, that something still needs to be done ... the better off we will be."

While some of the forgotten ashes in the basement of his funeral home date to the 1890s, some are more recent, Stefan said.

He recalled cremating the remains of a stillborn baby and giving the small brass urn to the mother. When the mother moved, she left the urn behind. The new tenant discovered it and returned the urn to Stefan, who was able to track down the mother.

"I told her what happened, she said, 'I'll call you back,"' Stefan said. "That was four or five years ago."