The parents of a seriously ill premature baby want her to have "every chance of survival", a court has heard.
Charlotte with her mother, Debbie, in hospital
Charlotte Wyatt weighed just one pound when she was born 11 months ago and has serious heart and lung problems.
Doctors believe her quality of life will be terrible, and want to let her die if she stops breathing again.
But David Wolfe, counsel for the parents, said they wanted the court to "hang on" to any real prospect for Charlotte.
He added they would like to look forward to taking their daughter out "so that she can have the feel of fresh air on her skin".
Darren, 32, and Debbie, 23, believe that, as she has survived this far, Charlotte must be given every assistance to help her live.
But doctors say she will not survive beyond infancy because her lungs are so severely damaged.
Charlotte was born when her mother was 26 weeks pregnant, has never left hospital and is fed through a tube as she cannot suck from a bottle.
She also needs a constant supply of oxygen.
David Lock, counsel for the hospital, part of the Portsmouth Hospitals NHS Trust, said a doctor had said she was "living in a plastic box" and that her life would be "dominated by pain and suffering".
Mr Lock summarised the trust consultants' findings by saying: "They are of the view that Charlotte has life-limiting conditions and that, despite their best efforts, she has no feelings other than continuing pain.
"Her quality of life is both terrible and permanent and they cannot see a way in which it would significantly improve."
He said one doctor had described her as "permanently sedated, living in a plastic box with a tube up her nose and blasted with gas".
Mr Lock added a consultant paediatric neurologist had said Charlotte "has no visual awareness and does not respond to sound... she does not respond to being cuddled and demonstrates no awareness of familiar persons."
David Wolfe, counsel for the Mr and Mrs Wyatt, said this part of the consultant's report was a matter of controversy.
Dr E, a specialist in paediatric respiratory medicine, who took over supervising Charlotte's care in August, said she was suffering from "the worst case of chronic lung disease I have ever seen".
The doctor added that Charlotte had lung scarring after having life-saving ventilation five times.
Portsmouth Hospitals NHS Trust says that while parents can decide what treatment is given to their child, they cannot insist on inappropriate treatment which would bring more suffering than benefits.
Ahead of the hearing, Mrs Wyatt told The Times newspaper: "It has all been very difficult for us.
"I just hope the judge makes the right decision. We want to cling to any chance we have."
Cases such as this are very rare, and are usually heard in private.
But, earlier this week, Mr and Mrs Wyatt - both committed Christians from Buckland, Portsmouth - were given permission for their case to be heard in public.
Trust managers agreed the case should be discussed openly so that it could reassure the public about the treatment it offered and the decisions it made.
At the preliminary hearing, the parents stressed that they maintained a good relationship with the trust, even though they disagreed with its view that Charlotte should not be ventilated if she needed it.
Mr Wolfe told the judge: "They are entirely happy with, and grateful for, the treatment which Charlotte has received so far from the trust and its staff."
The judge has banned the media from identifying the individual medical staff caring for Charlotte and the independent expert witnesses who are to be called to give evidence.
The case continues.