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Woody Allen’s controversial memoir has been released, weeks after it was pulped by its original publisher.

Apropos of Nothing was printed by Arcade Publishing in the US.

The previous publisher, Hachette, scrapped plans to release the book after protests from its staff and his children Ronan and Dylan Farrow.

Dylan has accused Allen of sexually abusing her in 1992 when she was seven years old. He denies the claim, calling it a "total fabrication" in his book.

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"I never laid a finger on Dylan, never did anything to her that could be even misconstrued as abusing her; it was a total fabrication from start to finish," he writes.

Describing a visit to his partner Mia Farrow's house, where he allegedly molested Dylan, he acknowledges briefly placing his head on his seven-year-old daughter's lap, but adds: "I certainly didn't do anything improper to her. I was in a room full of people watching TV mid-afternoon."

Arcade said it had decided to publish the autobiography as a matter of free speech.

"We find it critical to hear more than one side of a story and more importantly, not to squelch the writer's right to be heard," said Arcade's co-founder Jeannette Seaver in a statement.

"When speakers are shouted down or even assaulted on campuses for simply having a different point of view, journalists are banned from press conferences and truth is too often dismissed as 'fake news', we as publishers prefer to give voice to a respected writer and filmmaker, rather than bow down to the politically correct pressures of the modern world."

A spokesperson for the director said Allen had "told his story comprehensively in his book".

Dylan and her brother Ronan Farrow both criticised Hachette's original decision to publish the book.

Dylan called the memoir "deeply upsetting", while Ronan, a journalist who also recently released a book with the company, accused the publisher of concealing Allen's autobiography from him and its staff.

Hachette employees staged a walkout in New York and Boston to protest against the publication, and the company pulled the plug shortly afterwards.

A statement by Hachette at the time called the decision "a difficult one".

Allen is an Oscar-winning director who has written and directed cult classics including Annie Hall and Manhattan.

The 84-year-old lost a four-film deal with Amazon last November following comments he made about the #MeToo movement.