Fourteen-month-old Owen Targett had been affected by the rare and potentially fataldisease biliary atresia since birth.
He underwent a double operation in November to transplant his grandfather's donated liver. Six weeks after the transplant at Leeds Royal Infirmary, tests showed Owen has perfect liver function.
Grandfather John Targett, 59, was found to be a perfect match after three other donated livers were unsuitable.
Mr Targett said: 'It's absolutely brilliant. I would have no hesitation in doing it again.'
The once-poorly toddler is now fit and active. His proud grandad told reporters:
'You wouldn't recognise this baby from a month or two ago, he has really put on weight and feels heavy when I pick him up. He used to have little stick-like arms and legs and now he's walking. He'll soon be running and trying to talk as well.'
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Would you donate an organ for a relative without hesitation?