Haploidentical Hematopoietic Cell Transplantation Using TCR Alpha/Beta and CD19 Depletion

Inclusion Criteria: 1. Lack of suitable conventional donor (10/10 HLA matched related or unrelated donor) or presence of rapidly progressive disease not permitting time to identify an HLA-matched unrelated donor. This does not include cord blood unit (CBU) availability. 2. Lansky/Karnofsky score \> 50 3. Signed written informed consent 4. Diagnosis of one of the following: 1. Patient with life threatening hematological malignancy including "high-risk" ALL in first complete remission (CR1); ALL in second or subsequent remission (greater than or equal to CR2); high-risk AML in CR1; AML in second or subsequent CR; myelodysplastic syndromes (MDS); non-Hodgkin's lymphomas (NHL) in second or subsequent remission (greater than or equal to CR2); CML 2. Hemophagocytic Lymphohistiocytosis (HLH) including familial HLH, relapsed HLH or central nervous system (CNS) HLH 3. Primary Immunodeficiency Disorders (PID) 4. Hemoglobinopathies including thalassemia or sickle cell disease (SCD) 5. Severe aplastic anemia (SAA) not responding to immune suppressive therapy 6. Congenital/hereditary cytopenias including Fanconi anemia (FA) without malignant clonal evolution (MDA, AML) 7. Other inherited bone marrow failure syndromes (IBMFS) 8. Sever chronic active Epstein Barr virus infection (SCAEBV) with predilection for T-or NK-cell malignancy NOTE: 'High risk' ALL or AML refers to those acute leukemias identified by the presence of specific biologic features, which predict high likelihood of failure to conventional chemotherapy. As biologic features of high-risk disease evolve with improvement of conventional chemotherapy, it is not practical to define this indication with any further specificity. Therefore, high risk AML/ALL will be determined by the primary physician. Exclusion Criteria: 1. Life expectancy of less than or equal to 6 weeks 2. Greater than grade II acute graft versus host disease (GVHD) or chronic extensive GVHD due to a previous allograft at the time of inclusion 3. Subject receiving an immunosuppressive treatment for GVHD treatment due to a previous allograft at the time of inclusion 4. Symptomatic cardiac disease or left ventricular shortening fraction less than 25% or ejection fraction \< 40% 5. Severe renal disease, with creatinine clearance \< 40cc/1.73m2 6. Pre-existing severe restrictive pulmonary disease, FVC \< 40% of predicted 7. Severe Hepatic Disease with ALT/AST ≥ x 2.5 upper limit of normal or bilirubin level ≥ x 1.5 upper limit of normal 8. Serious concurrent uncontrolled medical disorder or mental illness 9. Pregnant or breastfeeding female subject 10. Current active infectious disease including viral and fungal diseases at the time of enrollment; that on evaluation of PI precludes ablative chemotherapy or successful transplantation 11. Active HIV infection 12. Severe personality disorder or mental illness that would preclude compliance with the study