TCR Alpha/Beta and CD19-deplete Haplo-HSCT

Inclusion Criteria: 1. Age 31 days to \<30 years 2. Have a malignant or non-malignant hematologic disease, defined as disease resulting from abnormal function of a cell of the hematopoietic stem cell lineage, that could benefit from an allogeneic HCT. Examples include acute and chronic leukemias, myelodysplastic syndrome, lymphoma, severe acquired and congenital cytopenias/marrow failure, white blood cell abnormalities, red blood cell abnormalities, and platelet abnormalities. 3. Clinical remission for patients with acute leukemia (MDS/AML excluded) or lymphoma 4. Lack a healthy and willing HLA-identical related donor, with the exception of patients with FA who will be eligible with a willing HLA-identical related donor given the standard use of T-cell depletion in matched sibling donor HCT in FA 5. Have a related or an unrelated donor who meets the donor selection criteria, is healthy, willing, and able to receive GCSF with or without Plerixafor, and undergo apheresis through placement of catheters in the antecubital veins or a temporary central venous catheter 6. Able to give informed consent if ≥ 18 years, or with legal guardian capable of giving informed consent if \< 18 years 7. Provision of signed and dated informed consent form Exclusion Criteria: 1. Uncontrolled, active infection at time of HCT 2. HIV positivity 3. Cardiac ejection fraction \<45% 4. Creatinine clearance \<60 mL/min/1.72 mL 5. Pulmonary diffusion capacity (adjusted for hemoglobin), FEV1, or FVC \<60% of predicted or an O2 saturation \<94% on room air if unable to perform pulmonary function testing 6. Serum ALT \>5x upper limit of normal or bilirubin \>2 7. Performance score (Lansky or Karnofsky) \<50 8. Pregnant or lactating females, as many medications necessary for a successful HCT are potentially harmful to unborn babies and infants.