Allogeneic hematopoietic cell transplantation (allo-HCT) is a potentially curative therapy for patients with hematologic malignancies including acute myeloid leukemia (AML), myelodysplastic syndrome (MDS), and acute lymphoblastic leukemia (ALL); however, human leukocyte antigen (HLA)-matched donor availability continues to be a major hurdle. Historically, HLA haploidentical donor hematopoietic cell transplantation (haplo-HCT) was associated with high incidences of graft rejection and excessive non-relapse mortality (NRM), but recent advances utilizing post-transplant cyclophosphamide (PT-Cy) have revolutionized haplo-HCT and the outcomes are now comparable to allo-HCT using more traditional HLA matched related and unrelated donors. However, graft-versus-host disease (GvHD) continues to be a problem and is associated with significant morbidity and mortality in allo-HCT patients including those who receive haplo-HCT on PT-Cy platform. The aim of this early phase study is to investigate the safety and overall efficacy of azacitidine in reducing the incidence and severity of GvHD when added to PT-Cy based haplo-HCT platform for patients with AML, ALL, or advanced MDS.