From my experience on the transplant service at our school...
Kidney transplants are usually about 4-5 hour affairs on average to put the organ in. To harvest it, you have to go to another hospital before that, where the harvest is anywhere btw. 2-4 hours long (depends on how many organs are coming out of the donor). Then you transport the organ to your site and immediately put it in. With kidneys there's a little more leeway, because they have a longer cold ischemia time than other organs such as heart and lungs.
For heart/lung transplants, due to the short amount of time that the organs can withstand, one team goes to collect the organ at the donor hospital, while a second team prepares the recipient at your hospital. The donor run that I did started at 2pm to go retrieve the lungs, by 8:30pm we were back in our hospital with the organ (meanwhile the other team prepped our recipient to the point where his lung was about to come out), and then we put the lung in, which took until about 2:30-3am in the morning. BTW, the previous posts were right. Most transplants happen in the evening/during the night, and there is significant close followup that needs to be done due to the chance or organ rejection and the side effects from the immunosuppressive drugs the recipients get.
and this is just the barebones of your responsibility as the surgeon. they also automatically participate in all the follow-up clinics, the coordination of the organ donation and selection of recipients, etc...
Hope that sheds some light on things.
BTW, it's pretty amazing when you see the new kidney hooked up to the iliacs, the clamp comes off, and you get this nice purple color going, and the ureter starts making urine right away. Not to mention when you see a new lung or a new heart start working/beating in the patient's chest.
