Phase 1/2: CD45RA Depleted Stem Cell Addback to Prevent Viral or Fungal Infections Post TCRab/CD19 Depleted HSCT

Inclusion Criteria: 1. Disease for which allogeneic HSCT may be curative. 2. Remission status of hematologic malignancies and additional disease-specific eligibility determinations will be according to standards of practice within the CHOP Cellular Immunotherapy and Transplant Program (CTTS). 3. Patients must be 25 years of age and less 4. Evaluation for organ and infectious status as per our CTTS standard operating procedure. 5. Signed consent by parent/guardian or able to give consent if 18 years of age and older. 6. Participants of childbearing potential must have a negative pregnancy test as per institutional SOP. Exclusion Criteria: 1. Patients who have performance score less than 60. 2. No suitable donor available for mobilized peripheral stem cells. 3. Patients with Hodgkin lymphoma or non-Burkitt, non-lymphoblastic lymphoma. 4. Planned receipt of alemtuzumab during conditioning. 5. Patients with an available 10/10 HLA matched sibling donor. 6. Patients who do not meet institutional disease, organ or infectious criteria. Donor selection and eligibility: 1. Unrelated donor meets National Marrow Donor Program criteria for donation. 2. Related donor (at least haploidentical) willing and able to donate mobilized peripheral stem cells. 3. HLA testing/matching * HLA testing to be done by molecular methods for A, B, C, DRB1, DQB1 * Related donor: Must be ≥ 5/10 match * Unrelated donor: 10/10 or 9/10 match * KIR typing for haploidentical donor for hematologic malignancies * Donor specific HLA antibodies (DSA) should be assessed for all subjects receiving an HLA mismatched graft (≤ 9/10). 4. Donor must be willing to undergo granulocyte colony stimulating factor (GCSF) mobilization and peripheral blood stem cell collection 5. Donors must be willing to sign consent to participate in this study.