From what I understand, it is almost impossible. The recipient needs to go on a waiting list, and there may well be hundreds of people inthe queue, in front of him.
He then needs to be tissue type matched to an available organ... I believe that this is done centrally, rather than locally, which makes it easier to find the right organ for the right patient.
Then, you have to make sure the donor is dead. Sounds silly, but, there are specific criteria to be met, before you can go breaking for spares.
There are three phases in the diagnosis of brain stem death:
1. Exclusion of reversible causes of coma and diagnosis of cause of irreversible brain damage.
2. Testing for destruction of brain stem components.
3. Confirmation of inability to breath spontaneously.
Once the diagnosis has been made, the cadaver can become an organ donor, providing that:
There is no reason to suppose that in life the individual had expressed any objection, and...
There is no objection from the nearest available relative(s)
Then the organs have to be anaesthetic free, and screened for nasties such as HIV, Hepatitis B and C.
All that takes time, and planning, which, IMO, makes spontaneous donation even more unlikely.
Source and further info:
http://www.rcgp.org.uk/default.aspx?page=2261 copy