John Travolta's 16-year-old son was "spectacularly supervised" before he was found collapsed at the family's vacation home on Grand Bahama, a lawyer for the actor said Sunday.

Travolta himself, in his first public statement since Jett's death, thanked people for their support and said he and his wife were "heartbroken that our time with him was so brief."

Police Superintendent Basil Rahming has said a caretaker found Jett Travolta unconscious in a bathroom late Friday morning before he was pronounced dead at a Freeport hospital.

The youth was last seen entering the bathroom on Thursday, according to Rahming's police statement.

But Travolta lawyer Michael McDermott said he doesn't believe that Jett was in the bathroom for a substantial amount of time.

"The police left the impression that the boy was unsupervised. No. There were two nannies with him for the entire evening," McDermott told The Associated Press. "They made it seem like he was sent to the condo and nobody checked in on him until the next morning."

"(Jett) was spectacularly supervised," said McDermott, who said he has not had the chance to talk to the two nannies himself.

McDermott said he had no knowledge of Jett's medical history but "understood he had a history of seizures." It is unclear whether Jett was taking medication for that.

The Bahamas' health minister, Dr. Hubert Minnis, has said that a second, U.S.-certified pathologist would fly in at dawn Monday to assist with the teenager's autopsy.

"I have spoken to (Travolta) and informed him that the government is doing everything it can," Minnis said Sunday, adding he could not disclose further specifics about the autopsy.

About a dozen security guards and Bahamian police officers patrolled Sunday around the luxury Old Bahama Bay resort community where Travolta and his wife, Kelly Preston, remained inside their home. The white-sand beach in front of the suites was closed.

The couple also has an eight-year-old daughter, Ella Bleu.

In a statement posted Sunday on Travolta's website, the couple said Jett was the "most wonderful son that two parents could ever ask for and lit up the lives of everyone he encountered."

"We will cherish the time we had with him for the rest of our lives," they said.

Travolta, 54, is trying to finish funeral arrangements and hopes to fly his son's body to Florida by midweek, McDermott said. Travolta and Preston, 46, have a house in Ocala, Fla.

Preston and Travolta have said that Jett became very sick when he was two years old and was diagnosed with Kawasaki Syndrome, an illness that leads to inflamed blood vessels in young children. Preston blamed household cleaners and fertilizers, and said that a detoxification program based on teachings from the Church of Scientology helped improve his health, according to People magazine.

The Church of Scientology, established in 1945 by science fiction writer L. Ron Hubbard, has attracted numerous celebrity followers, and among its more famed members is Travolta, who has long been one of Hollywood's biggest names.

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