Additional Study Information: The primary objective of this study is to determine if an HIV-infected donor liver (HIVD+) transplant is safe with regards to major transplant-related and HIV-related complications. This study will evaluate if receiving a liver transplant from an HIV-infected deceased liver donor is safe with regards to survival and major transplant-related and HIV-related complications compared to receiving a liver from an HIV-uninfected deceased liver donor (HIVD-). Those participants who have accepted a HIVD- organ will be randomized to be followed in the full study or followed in the nested observational group.