Alfie Evans was born in May 2016 with a degenerative neurological condition which doctors have not been able to definitively diagnose.
His parents, Tom Evans and Kate James, want him to have continued treatment, but doctors argue it would be "futile".
In the High Court in Liverpool today, the hearing had to be adjourned for 20 minutes for Mr Evans' parents and sisters to comfort him, as he wept while he heard evidence that life support should be turned off.
The parents of the 20-month-old believe he responds to them, but medics have said he is suffering spontaneous seizures as a result of being touched.
Michael Mylonas QC, representing the hospital, said: "One of the problems of this case is they look at him and, barring the paraphernalia of breathing and feeding, he's a sweet, lovely, normal-looking boy who opens his eyes, will smile..."
Mr Evans, 20, broke down when he heard this evidence, and a break was called in proceedings.
Mr Mylonas later continued by saying Alfie had suffered "catastrophic degradation of his brain tissue" and could only breathe with intervention.
He regularly has fits, triggered by touching.
At the request of Mr Evans and Ms James, three medical experts from the Vatican-linked Bambino Gesu Pediatric Hospital in Rome had visited but they had reached the same conclusions of "complete futility" of treating the baby.
Mr Justice Anthony Hayden, hearing the case, said he'd had the "privilege" of meeting Alfie, and added no one could blame the parents for trying to leave no stone unturned.
Medical experts are unable to say how aware of his surroundings Alfie is, and say if he can feel a soothing hand he may also feel a the "pin prick" during his treatment.
Italian experts suggested operations including a tracheotomy and a gastronomy to help him breathe and feed for an undefined period of time.
But an expert in the ventilation of children, believed such operations were "inappropriate".
He said: "I think we are all agreed from the medical perspective that life expectancy is limited.
"Because of that, I would feel it would be more appropriate to allow nature to take its course.
"That view is also supported by the fact that I don't think anyone can be certain exactly what Alfie is feeling and whether or not he maybe feeling pain or discomfort.
"I think the provision of continuing intensive care to sustain life when they may be suffering is not one that, as medical professionals, most would consider appropriate."
The hearing will continue on Friday.