Treosulfan/Fludarabine/Low Dose TBI as a Preparative Regimen for Children With AML/MDS Undergoing Allo HCT

Inclusion Criteria: 1. Age \< 21 years. 2. Disease and disease status: * Acute myeloid leukemia (AML) in morphologic remission (defined as \< 5% blasts in a bone marrow aspirate of adequate cellularity performed within 28 days from start of conditioning). * Myelodysplastic syndrome (MDS): Any 2008 WHO classification subtype (Appendix I). RAEB-2 patients may proceed directly to transplant, but may also be considered for induction chemotherapy before transplant. Patients with ≥20% morphologic marrow blasts will require induction therapy to reduce morphologic marrow blasts below 5% before transplant. 3. Karnofsky Index or Lansky Play-Performance Scale \> 70 % on pre-transplant evaluation. Karnofsky scores must be used for patients \> 16 years of age and Lansky scores for patients \< 16 years of age. 4. Able to give informed consent if \> 18 years, or with a legal guardian capable of giving informed consent if \< 18 years. 5. Negative pregnancy test (serum, urine β-HCG, or other test per institutional guidelines) for females of childbearing potential. 6. A single previous autologous or allogeneic HCT is allowed as long as the time from first to second transplant hematopoietic cell infusion is no less than 6 months. 7. With a suitable allogeneic hematopoietic cell donor including, as available: * HLA-identical related donor matched for HLA-A, and -B at the serologic level at minimum and -DRB1 at high resolution by molecular typing. A single locus mismatched related donor (7/8 matched) is permitted only if there are no 8/8 matched unrelated donors available. * Unrelated volunteer donor matched for HLA-A, -B, -C and -DRB1 defined by high resolution molecular typing. A single HLA antigen or allele mismatch (7/8 matched) is permitted. * Unrelated cord blood (UCB) matched to the recipient at a minimum of 4 of 6 loci at HLA-A, and -B by intermediate resolution and -DRB1 by high resolution. Cord blood unit(s) will be selected using the following criteria: 1. Unit selection is based on the cryopreserved total nucleated cell (TNC) dose and matching at HLA-A, -B intermediate resolution and -DRB1 high resolution typing. While HLA-C antigen/allele level typing is not considered in the matching criteria, if available, it may be used to optimize unit selection. 2. Selection of two UCB units is required if a single UCB unit will not provide a sufficient cell dose (see Table 1 below). When two UCB units are not required per Table 1, two UCB units may be used with approval of the study chair or designee. When two units are selected, the following rules apply: * The UCB unit with the least HLA disparity with the patient, followed by the larger cell dose for equivalently matched units, will be considered unit #1 (selection priority is 6/6 match \>5/6 match\>4/6 match). * An additional UCB unit may be required to achieve the required cell dose, as outlined in the table below. The second unit will be the one that most closely HLA matches the patient and meets minimum size criteria as outlined below (i.e. a smaller and more closely matched unit will be selected over a larger less well matched unit as long as minimum cell dose criteria are met). * Each UCB unit MUST contain at least 1.5 x 10\^7 TNC per kilogram recipient weight. 3\) Other comments about cord blood unit selection: * Use of unlicensed cord blood units will adhere to current federal regulatory requirements for procurement. * Units will be selected based on the TNC dose and HLA matching. * A UCB unit that is 4/6 or 5/6 mismatched but homozygous at the locus of mismatch should be chosen over a 5/6 unit with bidirectional mismatch even if the latter unit provides a larger cell dose. This is only applicable to choosing units within a given match grade. * Within the best HLA match grade, the unit containing the greatest number of cells will be chosen. If there are two units of equivalent cell dose within a match level, choose the unit with best match by higher resolution molecular typing, if known. * Other factors to be considered: i. Within the same HLA match grade, matching at both DR loci is preferable. ii. UCB units sourced from cord blood banks located in the United States are preferred. iii. Younger units are preferred over older units, all other factors being equal. 8. Adequate organ function, defined as: * Pulmonary: FEV1, FVC, and corrected DLCO must all be ≥ 50% of predicted by pulmonary function tests (PFTs). For children who are unable to perform for PFTs due to age, the criteria are: no evidence of dyspnea at rest and there is no need for supplemental oxygen. * Renal: GFR estimated by the updated Schwartz formula ≥ 90/min/1.73 m2, i.e. height (cm)/serum creatinine (mg/dl) \> 220. If the estimated creatinine clearance is \< 90 ml/min/1.73 m2, then renal function must be measured by 24-hour creatinine clearance or nuclear GFR, and must be \> 70 mL/minute/1.73 m2 * Cardiac: Shortening fraction of ≥ 27% by echocardiogram or radionuclide scan (MUGA) or ejection fraction of ≥ 50% by echocardiogram or radionuclide scan (MUGA) * Hepatic: SGOT (AST) or SGPT (ALT) \< 5 x upper limit of normal (ULN) for age; Conjugated bilirubin \< 2.5 mg/dL, unless attributable to Gilbert's Syndrome. 9. Co- enrollment in PBMTC ONC 1001 (CIBMTR 09-MRD) protocol and/or CIBMTR 10-CBA protocol (NMDP cord blood IND) is allowed. Co-enrollment on any other studies where experimental therapy is being administered will be handled on a case-by-case basis and must be discussed with the study chair or designee prior to enrollment. Exclusion Criteria: 1. Pregnant or lactating females are ineligible as many of the medications used in this protocol could be harmful to unborn children and infants. 2. Patients with HIV or uncontrolled fungal, bacterial or viral infections are excluded. Patients with history of fungal disease during induction therapy may proceed if they have a significant response to antifungal therapy with no or minimal evidence of disease remaining by CT evaluation. 3. Patients with active CNS leukemia or any other active site of extramedullary disease at the time of enrollment are not permitted. Note: Those with prior history of CNS or extramedullary disease, but with no active disease at the time of pre-transplant workup, are eligible. 4. Patients undergoing a course of chemotherapy using another investigational drug. 5. Patients diagnosed with Fanconi Anemia.