So can elements of a person's character - or even their soul - be transplanted along with a heart?
One woman who believes this to be the case is CLAIRE SYLVIA, a divorced mother of one.
She was 47 and dying from a disease called primary pulmonary hypertension when, in 1988, she had a pioneering heartlung transplant in America.
She was given the organs of an 18-year-old boy who had been killed in a motorcycle accident near his home in Maine.
I made it perfectly clear to him from the moment he mentioned he was in a new relationship that my son was not to be part of it. In an email which was ironing out other issues of access, maintenance, calendar synchronisation, school meetings and the 101 other things you suddenly have to deal with as separated parents, I added a terse line saying: ‘I do not want our son sharing his time with you with third parties.’By which of course I did not mean his granny, his aunties, cousins or friends we have known for years.I can still picture the look on his face when, during one particularly heated discussion over access and childcare arrangements, I told him that if he continued to be difficult I would simply move away, get married, have more children and he would have to deal with another man being ‘Daddy’.Friends have warned me that when my son is older, he might want to spend more time with his father and ask to meet whoever it is my ex is then seeing."This sometimes happens with the lungs, which are very fragile. Sometimes, at the last minute, things don't work out." I looked up at him and said: "That's OK. It's in God's hands now." After that, I don't remember anything until slowly becoming aware of a buzz of voices calling my name: "Claire, wake up.It's over." I awakened gently, feeling no bodily or physical sensation - nothing but pure consciousness and a cacophony of voices.