This trial is a phase II, single arm, open-label, single center pilot study to assess a reduced-intensity conditioning regimen, bone marrow transplantation and high dose post-transplantation cyclophosphamide (PTCy) in recipients of a partial liver allograft from a Human Leukocyte Antigen (HLA)-matched or -haploidentical living related donor in patients with HCC. The trial includes analyses of tumor characteristics and the number and phenotype of tumor infiltrating lymphocytes in the explanted tumor. The trial also includes periodic monitoring of circulating hepatocytes to correlate with tumor response.