Surgeons were due to complete the long and complex operation to separate Siamese twins Jodie and Mary late last night.
A team of 20 medics had been working since 9am to separate the twins at St Mary's Hospital, Manchester, where they were born in August.
The operation, which will end the life of the weaker twin, Mary, but should allow Jodie to lead a relatively normal life.
Their parents, from the Maltese island of Gozo, have practically lived at the hospital since the birth and were waiting for news.
Security officers were drafted in to stand guard in the corridors outside the theatre. Three protestors staged a peaceful demonstration outside the hospital for most of the day.
The legal battle to save Jodie began shortly after the twins were born with fused spines, joined at the abdomen and with their arms and legs at right angles to their upper bodies.
Mary, who has primitive brain functions, was said to be "draining the life" out of Jodie, who was thought to have normal mental functions.
Doctors from the hospital went to the High Court in August and won the right to operate despite the objection of their parents, who are strict Roman Catholics.
They did not want the operation to go ahead for religious reasons, believing nature should be allowed to take its course.
The parents challenged the decision in a privately-funded appeal the following month, but lost.
An 11th hour appeal was lodged by the ProLife Alliance last Friday, but it also failed to halt the surgery.
A spokesman for the ProLife Alliance said: "The right to exhaust all legal defence avenues would not be withheld from a criminal on death row anywhere in the democratic world, but has been withheld in Britain from an innocent child.
"Mary's life is being extinguished, not because she is a conjoined twin, not because her heart beats inadequately, not because Jodie's life is under threat, but because she is mentally impaired and her life is deemed of no intrinsic value."
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