Joan Rivers Dead -- Legendary Comedienne Dies at 81

Joan Rivers -- who made the world laugh for over 50 years with her jokes, put-downs and one-liners -- has died in NYC ... a week after her heart suddenly stopped beating during vocal cord surgery.

She was 81.

Joan's daughter Melissa Rivers took her mom off life support so she could pass comfortably in a private room.

The death has been reported to the NYC Medical Examiner's Office -- and officials tell TMZ the office will open an investigation to determine cause of death.

Melissa just issued a statement saying, "It is with great sadness that I announce the death of my mother, Joan Rivers."

"She passed peacefully at 1:17 PM surrounded by family and close friends. My son and I would like to thank the doctors, nurses and staff of Mount Sinai hospital for the amazing care they provided for my mother."

"Cooper and I have found ourselves humbled by the outpouring of love, support and prayers we have received from around the world. They have been heard and appreciated."

"My mother's greatest joy in life was to make people laugh. Although that is difficult to do right now, I know her final wish would be that we return to laughing soon."

Rivers is widely credited for opening doors for countless female comediennes. She broke through in a big way during her appearances on "The Tonight Show" with Johnny Carson.

She also famously enraged Carson by accepting a gig to host a competing late night show on FOX. Carson never spoke to her again.

Rivers was born in 1933 -- she worked as a writer and fashion consultant before entering show biz as a stand-up comic in the early '60s. She was famously self-deprecating ... often self-critical of her looks and her marriage to Edgar Rosenberg ... who committed suicide in 1987.

Joan's late '80s FOX show tanked, which somewhat derailed her career. It was resurrected in a big way in 2010 in the wake of the documentary "Joan Rivers: A Piece of Work."

She was universally adored by fellow comedians, including fellow legend Don Rickles, who once said about her ... "Joan is not only a very intelligent lady, but extremely masterful at comedy timing. Sharing the stage with her has always been a joy for me."

Barbara Walters was asked about Joan last year, saying ... "I wouldn't dare to try to be funny about Joan Rivers because she is the smartest, best-informed and funniest woman I know."

Joan and her daughter Melissa began working as a team hosting various red carpet and fashion shows on E! and other networks, including "Fashion Police."

Joan's credits could fill a book ... including appearances in "The Muppets Take Manhattan," "The Carol Burnett Show," "Hollywood Squares," "Pee Wee's Playhouse," "Celebrity Apprentice," "Saturday Night Live" ... and on and on.