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The number of organ donors in Wales will increase by about a quarter under a change to the law, the Welsh government estimates.

It published legislation on Monday to introduce the UK's first opt-out organ donation system.

People will be deemed to have consented to becoming donors unless they opt out of the organ donor register.

Officials say it could mean 15 extra donors leaving around 45 more organs for transplant every year.

They add that the money saved by one transplant will be enough to pay for all of the changes.

Families will not have a legal veto over the wishes of dead loved ones, but they will be able to stop organs being removed in practise.

The Welsh government says the process will not be able to go ahead unless families give their assistance to medical staff who want to take a relative's body into a theatre.

The current situation where people must die in hospital to be eligible as a donor, even if they are on the register, will stay the same.

Around 30,000 people die in Wales every year. But in 2010/11 only 228 were potentially suitable to be donors and of those 67 actually left organs for transplant.

Officials say that international evidence suggests families are less likely to stop organs being removed in countries with opt out systems.

They hope to see an increase of 25 - 30% in the number of donors meaning an extra 45 organs every year.

Organs will be available for transplant to anyone in the UK on a waiting list, not just Welsh patients.

The law will apply to anyone over 18 who has lived in Wales for at least six months.

The length is intended to be long enough for people to know about the law and to opt out if they want to.

Health Minister Lesley Griffiths said despite a 49% increase in donation rates since 2008, 37 people died in Wales while waiting for an organ last year.

She said: "I believe the time has come to introduce a change in the law together with an extensive communication and education programme encouraging people to make a decision and to ensure their families know their wishes."

The Law Society has previously called for more clarity from the Welsh government on what role will be left for families when a relative dies.

The draft Human Transplantation (Wales) Bill follows a public consultation, which ministers say found support for their plans.

Once it passes through the assembly the new system could be in place by 2015.

With 300 people on the transplant waiting list, the Welsh government wants to improve the rate of organ donation.

But the Church in Wales, the Roman Catholic Church in Wales and the Wales Orthodox Mission have called for a re-think, with other critics saying there is no evidence that changing the law will work.

In a statement, the Bishops of the Church in Wales said Christians should be encouraged to join the donor register, but organ donation was an "altruistic gift" that should be "freely given, not assumed".

"It would be better to invest resources in wide-reaching public awareness campaigns to encourage more people to become voluntary donors," they said.

"Evidence that any system of 'automatic' donation increases the supply of organs - whether it's called 'presumed' consent, 'deemed' consent, or 'opt-out' - is still disputable."

Dr George Findlay, chair of the Welsh Organ Donation and Transplantation Committee, and a consultant in intensive care at Cardiff's University Hospital of Wales, said: "As a doctor we are not going to do anything against family wishes.

"It is a terrible time to talk to families. It helps if you know what a patient's wishes are.

"If patients haven't opted out we would hope to talk to families about what organ donation is and the fact that their family has expressed to be an organ donor and, hopefully, that could be followed through.

"The role of the family is crucial and essential and will not change under this legislation."

He said the appointment of a specialist organ donation nurse at every hospital was a key part in improving Wales' organ donation rate over the last four years.

But he said it was hoped those figures could improve further over time because the biggest "obstacle" is lack of family support after their relative dies which he hoped the new legislation would help to resolve.

Plaid Cymru supports the proposals, but Conservative AMs will be allowed a free vote on the Bill when it comes before the assembly.

Shadow health minister Darren Millar said: "It remains a fact that some countries operating presumed consent systems have lower rates of organ donation so legislation should not be seen as a silver bullet to improving donation rates."