Hello: Sec1205,
You have an interesting question:

For a live donor Kidney to be successfully accepted for a recipient.

There are few things that need to be considered:
- The PRA has to be as low as possible (Panel reactive antibody). (in our case (my wife donor PRA = 0)
- Preferably (not mandatory) some match in the Class II HLA domain (assuming the donor is not you sibling), If you are siblings then you will get one or more HLA matches (provided both have the same parents)

Assuming PRA reaction is in acceptable levels set by the transplant center, then the elaborate testing begins.
- Such as: How healthy both are you (donor & recipient) any existing medical issues, medications ( diabetes, Cardiac health). Can both of you withstand the surgical stress, hazard ratios etc

So within the domestic US, The standards for approval process are quite elaborate & robust and on top of it each Transplant center has it own standards & guide lines.

Best