With organ donation, what other things have to match, aside from the histocompatibility complex?

Blood group: Matching ABO blood groups is even more important in most transplants.

Size for some organs: For some organs that are transplanted orthotopically (into the native anatomic location), the size of the donor organ must be reasonably close to that of the recipient's own organ. This includes heart, lung and liver transplants. Kidneys are different since they are transplanted heterotopically (into a different space than the normal anatomic location) which leaves lots of room for adjustment.