As far as folks visiting a patient after surgery, everybody is different. Over the years I've had numerous surgeries, I don't like to have a lot of visitors. When I'm sick or recovering, I like to sleep and not engage in conversation. I love my brother, but he always shows up when I've left recovery and just put in a room. Then he wants to laugh and joke, and it is exhausting trying to talk when your weak or in pain. Plus, he gets loud and disturbs the other patients. When I've asked him to lower his voice, that's his cue to step it up.
The last time I had surgery it was performed on a Monday but he thought it was going to be Wednesday. I just called when I got home, and told him they had a sudden opening and I didn't have time to call to tell him. I know that sounds like I'm a terrible sister, but the last surgery left me in terrible pain and I just couldn't deal with him trying to entertain the hospital staff and other patients while I felt so sick.
But other people like visitors because it cheers them up. Especially if it's a long term stay, visitors break up the monotony. I'm not sure how long the hospital stay is for transplants, but I'm guessing the donor gets to go home earlier.
I just thought of something else, you can always arrange for a dinner or lunch for the family, even after everybody is home. It will lighten their load a little. If other friends and relatives want to help, see if you can find out who is coordinating efforts, and volunteer to help. Sometimes just having someone stop by to walk your dog is helpful.