This is a multicenter, interventional and observational study to understand factors affecting the likelihood of transplantation in patients without a human leukocyte antigen (HLA) matched family donor and to compare outcomes associated with pursuing an HLA-identical unrelated versus other alternative donor graft sources. Alternative donors are defined as any donor other than an HLA-matched or 1 antigen-mismatched related donor. Patients with acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), myelodysplastic syndromes (MDS), Non-Hodgkin lymphoma (NHL), Hodgkin lymphoma (HL), acquired aplastic anemia (AA) or sickle cell disease (SCD) are eligible. The primary comparison for the interventional study will be between two arms based on biologic assignment, analyzed on an intention-to-treat basis: Arm 1: Patients who are Very Likely to find a matched unrelated donor (MUD), defined as having a >90% chance of finding an 8/8 HLA-matched unrelated donor, for whom a fully matched unrelated donor will be pursued; and Arm 2: Patients who are Very Unlikely to find a MUD, defined as having a <10% chance of finding an 8/8 HLA-matched unrelated donor, for whom a haploidentical, cord blood, or mismatched unrelated donor transplant will be pursued. Patients with a Less Likely chance of finding a MUD, i.e., those not falling into the other two groups (a 26% chance), will be enrolled onto the observational component of the study and analyzed for all relevant endpoints but will not be included in the primary comparison.