The number of units performing children's heart surgery in England will be cut to six or seven from 11, under NHS plans.
Experts say the recommendation will lead to safer services and will ensure doctors and surgeons are able to maintain their expertise.
Options which will form part of a consultation document are currently being discussed but all 11 units in England are affected.
The idea of cutting the number of units was first raised more than a decade ago following the Bristol baby heart scandal when children died needlessly.
An inquiry, led by Professor Sir Ian Kennedy, said children should have heart surgery in fewer centres, which would be more specialist.
A follow-up report published by Sir Ian today says not all 11 centres would be able to meet new clinical standards.
According to his study, the Evelina Children's Hospital in London is most able to meet the standards, but bottom of the list, just above Oxford's John Radcliffe, is Leeds General Infirmary.
The John Radcliffe has already stopped its operations following several deaths last year.
The move to cut the number of centres is supported by a range of organisations, including the Society for Cardiothoracic Surgery, the Royal College of Surgeons and the Royal College of Paediatrics and Child Health.
They believe change is needed because some centres cannot provide appropriate 24/7 care, and argue that cutting the number would lead to fewer deaths and complications.
They also point to wide variation in the expertise available at centres, and low caseloads which make it difficult to maintain and develop staff skills.
It is thought larger centres are better placed to recruit new surgeons and plan for future surgery.
But opponents say the changes mean parents will have to travel further to visit their very sick children and some units under threat are performing well.
The 11 units under review are: Alder Hey Children's Hospital, Liverpool; Birmingham Children's Hospital; Bristol Royal Hospital for Children; Evelina Children's Hospital, London; Freeman Hospital, Newcastle; Glenfield Hospital, Leicester; Great Ormond Street Hospital for Children, London; Leeds General Infirmary; Oxford John Radcliffe Hospital; Royal Brompton Hospital, London; Southampton General Hospital.
Under the recommendations, new Congenital Heart Networks will be developed across England to provide joined-up care for children with heart disease.
These will support them from antenatal screening through to adult services.
A new system for analysing death rates among children treated at the hospitals is likely to be brought in.
Each of the 11 centres at present has between one and four surgeons.
The recommendation in future is that each unit must perform at least 400 surgical procedures each year, and ideally 500.
Some 3,600 paediatric surgical procedures are performed in England each year.
In the foreword to his report Sir Ian said: "I first recommended that quality standards relating to children's congenital cardiac surgeries be developed and implemented in 2001 following a major public inquiry into an NHS child heart unit.
"I also recommended that medical and nursing expertise for children needing heart surgery should be concentrated in a smaller number of specialist units in the belief that only those centres can achieve and sustain the necessary excellence and quality.
"Sadly, there have been a number of false starts on the road to achieving these goals."
Options agreed at today's meeting will go to public consultation, which will run from February 28 to July 1.
Labour MP Hilary Benn is calling on the Government to keep open the unit at the Leeds General Infirmary, which he says serves the whole of Yorkshire and beyond.
"There is real danger that the Leeds unit will be earmarked for closure," he said.
"If this happens, it would mean worried parents and sick children having to travel elsewhere for treatment.
"I have seen for myself the great work that the team at the LGI unit do. We need to support them by keeping the unit open."
Jo Webber, deputy policy director of the NHS Confederation, said heart surgery for children was complex and challenging.
"A resolution to this issue is long overdue and we need to ensure that we get these kinds of decisions right and do not expose them to further delay.
"This is not about cuts to services or indeed the closure of centres because they are failing to do the best they can.
"It is about concentrating the very best skills and experience in a smaller number of locations where a truly world-class level of care can be provided for every patient."
A joint statement from the Royal College of Surgeons and the Society for Cardiothoracic Surgery said: "England has the right number of heart surgeons treating rare heart conditions in children, but we know that they are thinly spread over too many units.
"A better service would be provided if this expertise were condensed in fewer units with the critical number of staff to support each other, disseminate new techniques and train the next generation of specialists."
In the foreword to his report, Sir Ian said finding himself in 2010 "taking part in a process that first began with the public inquiry in 1998 gives me mixed feelings".
He said there was a need for people to put aside particular interests in favour of the greater good.
"During the current assessment process I and my colleagues on the panel found many examples of commendably high commitment and dedication by talented NHS staff delivering congenital cardiac services.
"But we found exemplary practice to be the exception rather than the rule.
"Mediocrity must not be our benchmark for the future."
Sir Ian's report is just part of the material currently under discussion.