His parents said that the youngster had defied doctors' expectations and they took their case to the Court of Appeal, but the application to take him overseas was rejected.
His dad, Tom Evans, posted on Facebook to say that he was "heartbroken", writing: "My gladiator lay down his shield and gained his wings at 2.30am. absolutely heartbroken".
A six-month battle with Liverpool's Alder Hey Children's Hospital saw medical staff allegedly targeted and a mob try to storm the hospital doors.
About 1,000 people gathered 12 hours after the boy died to release blue and purple balloons in solidarity with the grieving mother and father who had struggled to come to terms with their child's terminal illness. "Thank you everyone for all your support", his mother Kate James wrote. Trump has not mentioned Alfie's case. He began breathing unaided, prompting appeals by his parents to the High Court and then the Court of Appeal to allow their son to leave the country.
Cardinal Vincent Nichols, the most senior Catholic cleric in England and Wales said it was right for a court to "decide what's best not for the parents, but for the child".
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Alfie's parents, Tom Evans and Kate James, opposed withdrawing life support from the youngster, who had a degenerative brain disease, and wanted to take him overseas for treatment. "Today I pray especially for his parents, as God the Father receives him in his tender embrace". Rational action, spared of emotion, can be an expression of love; and I'm sure Alfie received this kind of care.
Tensions between the toddler's parents and the hospital had eased in recent days.
He confounded expectations by continuing to breathe unaided for days, but died in the early hours of Saturday, his parents said.
"He is still working, he's doing as good as he can", Evans said to The Telegraph.
He thanked the hospital staff "for their dignity and professionalism during what must be an incredibly hard time for them too". The statement from Alfie's father was surprising given the animosity that had developed between the Evans family and the hospital.
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"I would like to express my deepest sympathy at this moment of loss to Tom and Kate as we hold little Alfie in our prayers", said Archbishop McMahon. "This has been a devastating journey for them, and we would ask that their privacy and the privacy of staff at Alder Hey is respected".
Both cases were also influenced by opportunistic elements - in the Gard case, US lawmakers intent on rubbishing Obamacare, and in the Evans case, a controversial Christian pro-life body that is funding the legal challenge. When the view of the state and the view of a child's parents are at odds, who gets to have the final say?
Alfie's case has drawn worldwide attention, with officials in largely Catholic Poland and Italy implicitly criticizing Britain's courts and state-run National Health Service.
Archbishop Malcolm McMahon of Liverpool said he discussed the case personally with the pope and has assured him that Alder Hey had done everything "humanly possible" to help Alfie, according to an April 25 report in The Tablet magazine.
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