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Gandolfini and his wife Deborah, who were married in 2008, have a daughter Liliana, born last year, HBO said. The actor and his former wife Marcy have a teenage son, Michael.
New Jersey Governor Chris Christie said: "It's an awful shock. James Gandolfini was a fine actor, a Rutgers alum and a true Jersey guy. I was a huge fan of his and the character he played so authentically, Tony Soprano.
"I have gotten to know Jimmy and many of the otheractors in the Sopranos cast and I can say that each of them are an individualNew Jersey treasure.
"Mary Pat and I express our deepest sympathies to Mr Gandolfini's wife and children, and our prayers are with them at this terrible time."
Celebrities have been paying tribute to Sopranos star James Gandolfini, 51, who has died of a suspected heart attack whilst on holiday in Rome, Italy.
- James Gandolfini was best known for his Emmy-winning portrayal of New Jersey mob boss Tony Soprano in the acclaimed television series The Sopranos
- Since The Sopranos ended its run in 2007 he has appeared in espionage thriller Zero Dark Thirty and the comedy The Incredible Burt Wonderstone
- Gandolfini was working on an upcoming new HBO series Criminal Justice at the time of his death
Sopranos star James Gandolfini, 51, has died of a suspected heart attack whilst on holiday in Rome, Italy, HBO confirmed.
Latest ITV News reports
The entertainment world is in shock at the news of the death of James Gandolfini, best known for his role as mob boss Tony Soprano.