Cord Blood Transplant in Children and Young Adults With Blood Cancers and Non-malignant Disorders

Participant Inclusion Criteria: Age and Donor Status: Patients with age ≤ 21 years at time of consent with no available and suitably matched related or unrelated donor in the required time period. Diagnoses : I. Acute myelogenous leukemia (AML) : * Complete first remission (CR1) at high risk for relapse such as any of the following: * Known prior diagnosis of myelodysplasia (MDS) or myeloproliferative disorder (MPS). * Therapy-related AML (t-AML). * White cell count at presentation \> 100,000. * Presence of extramedullary leukemia at diagnosis. * Any unfavorable subtype by FAB or WHO classification. * High-risk cytogenetics (e.g. those associated with MDS, abnormalities of 5, 7, 8, complex karyotype) or high-risk molecular abnormalities. * Requirement for 2 or more inductions to achieve CR1. * Presence of Minimal Residual Disease (MRD+) by cytogenetics, flow cytometry or molecular methods after induction. * Any patient with newly diagnosed AML with intermediate risk cytogenetics who elects allograft with curative intent over consolidation chemotherapy. * Any patient unable to tolerate consolidation chemotherapy as would have been deemed appropriate by the treating physician. * Other high-risk features not defined above. * Complete second remission (CR2). * Primary refractory or relapsed AML with less than 10% blasts by bone marrow morphology. Patients with cytogenetic, flow cytometric, or molecular abnormalities in ≤ 10% of cells are eligible. II. Acute lymphoblastic leukemia (ALL): * Complete first remission (CR1) at high risk for relapse such as any of the following: * White cell count at presentation \> 30,000 for B-cell lineage and \> 100,000 for T-cell lineage. * Presence of any high-risk cytogenetic abnormalities such as t (9;22), t (1;19), t (4;11) or other MLL rearrangements (11q23) or other high-risk molecular abnormality. * Failure to achieve complete remission (CR) after four weeks of induction therapy. * Persistence or recurrence of MRD on therapy. * Any patient unable to tolerate consolidation and/or maintenance chemotherapy as would have been deemed appropriate by the treating physician. * Other high-risk features not defined above. * Complete second remission (CR2). * Primary refractory or relapsed ALL with MRD disease after antibody therapy (e.g., blinatumomab, inotuzumab, other) and/or CAR-T cell therapy. III. Other acute leukemias: Leukemias of ambiguous lineage or of other types (e.g. blastic plasmacytoid dendritic cell neoplasm) with less than 5% blasts by BM morphology. Patients with persistent/relapsed disease with cytogenetic, flow cytometric or molecular aberrations in ≤ 5% of cells are eligible. IV. Myelodysplastic Syndrome (MDS) / Myeloproliferative Disorders (MPD) other than myelofibrosis: * International prognostic scoring system (IPSS) risk score of INT-2 or high risk at the time of diagnosis. * Any IPSS risk category if life-threatening cytopenia(s) exists. * Any IPSS risk category with karyotype or genomic changes that indicate high risk for progression to acute myelogenous leukemia. * MDS/ myeloproliferative disorder overlap syndromes without myelofibrosis. * MDS/ MPD patients must have less than 10% bone marrow myeloblasts and ANC ≥ 0.2 (growth factor supported if necessary) at transplant work-up. V. Non-Hodgkin lymphoma (NHL) or Hodgkin lymphoma (HL) at high-risk of relapse or progression if not in remission: * Eligible patients with aggressive histology (such as, but not limited to, diffuse large B-cell NHL, mantle cell NHL, and T-cell histology) in CR. * Eligible patients with indolent B cell NHL (such as, but not limited to, follicular, small cell or marginal zone NHL) will have 2nd or subsequent progression with stable disease/ CR/ PR with no single lesion equal to or more than 5 cm. * Eligible patients with HL will be those without progression of disease (POD) after salvage chemotherapy with no single lesion ≥ 5 cm. VI. Inherited Metabolic Disorders \[also see EBMT Handbook for discussion on patient eligibility for allogeneic transplant; in general, patients are considered early in the disease course, before they develop neurologic symptoms (46)\]: * Hurler Syndrome * Hunter (MPS 2 - early disease) * Sly syndrome (MPSVIII) * α-Mannosidosis * X- ALD * Osteopetrosis * Metachromatic Leukodystrophy * Globoid (GLD) VII. Non-Malignant disorders (other) \[also see EBMT Handbook for criteria for transplant (46)\] * Hemoglobinopathies * Bone Marrow Failure syndromes * Immunodeficiencies, including HLH Organ Function and Performance Status Criteria: * Karnofsky or Lansky score ≥ 70% (see Appendix) * Bilirubin ≤ 1.5 mg/dL (unless benign congenital hyperbilirubinemia). * ALT ≤ 3 x upper limit of normal. * Pulmonary function (spirometry and corrected DLCO) ≥ 50% predicted (corrected for hemoglobin) . * Left ventricular ejection fraction ≥ 50%. * Age-adjusted Hematopoietic Cell Transplantation-Comorbidity Index (aaHCT-CI) less than or equal to 7. * Renal: serum creatinine ≤ 1.5x normal for age. If serum creatinine is outside the normal range, then CrCl \> 50 mL/min/1.73m2 (calculated or estimated) or GFR (mL/min/1.72m2) \>30% of predicted normal for age. Normal GFR in Children and Young Adults (Age) : Mean GFR +- SD (mL/min/1.73 m2) 1 week: 40.6 + / - 14.8 2-8 weeks: 65.8 + / - 24.8 \>8 weeks: 95.7 + / - 21.7 2-12 years: 133.0 + / - 27.0 13-21 years (males): 140.0 + / - 30.0 13-21 years (females: 126.0 + / - 22.0 GFR, glomerular filtration rate; SD, standard deviation greater than 2 years old: Normal GFR is 100 mL/ min. Infants: GFR must be corrected for body surf ace area. For metabolic diseases: disease status to be evaluated according to EBMT Handbook \[45\]. Graft Criteria CB units will be selected according to the current MSKCC unit selection algorithm. High resolution 8 allele HLA typing and recipient HLA antibody profile will be performed. Cord unit selection will occur based on HLA-match, total