The finer details of this would perhaps draw more interest from the surgical crowd.
For the pragmatic intensivist, the most important questions are "where are the sites of anastomosis" and "how much liver is in there, and of what quality".
Orthotopic transplantation: you remove the whole recipient liver, and you put the whole donor liver into the normal anatomical position.
Auxiliary transplantation: Some of the recipient liver is removed, and a small incomplete donor graft is attached to the site. This has advantages in the context of acute liver failure - eventually, when the recipients native liver recovers, one may stop the immunesuppressant drugs, and allow the graft to be destroyes. The disadvantage is the complexity of the procedure- all sorts of vascular and biliary tree elements need to be completely reconstructed.
Sites of anastomosis:
Quality of the donated organ: