Inclusion Criteria:

1. Males and females aged > 1.0 year and < 66.0 years
2. Patients with acute leukemia in morphologic complete remission or with myelodysplasia (MDS) with no circulating blasts and with less than 5% blasts in the bone marrow. Patients with Chronic Myelomonocytic Leukemia (CMML) must have a white blood cell count ≤10,000 cells/µL and <5% blasts in the marrow.
3. Planned myeloablative conditioning regimen
4. Patients must have a related or unrelated donor as follows:
   1. Related donor must be an 8/8 match for human leukocyte antigen (HLA)-A, -B, and -C at intermediate (or higher) resolution, and -DRB1 at high resolution using DNA-based typing. Pediatric related donors must weigh ≥ 25.0 kg., must have adequate peripheral venous catheter access for leukapheresis or must agree to placement of a central catheter, must be willing to (1) donate bone marrow and (2) receive G-CSF followed by donation of peripheral blood stem cells (product to be determined by randomization post enrollment) and must meet institutional criteria for donation.
   2. Unrelated donor must be an 8/8 match at HLA-A, -B, -C and -DRB1 at high resolution using DNA-based typing. Unrelated donor must be medically eligible to donate according to National Marrow Donor Program (NMDP) (or equivalent donor search organization) criteria. At time of enrollment, the donor should not have any known preferences or contraindications to donate bone marrow or peripheral blood stem cells. (Selection of unrelated donors is to be performed according to institutional practice. It is recommended that the time from collection to initiation of the cell processing be considered when prioritizing donors, as data shows better results for CD34 selection when cell processing begins within 36 hours of the end of collection)
5. Cardiac function: Ejection fraction at rest ≥ 45.0% or shortening fraction of ≥ 27.0% by echocardiogram or radionuclide scan (MUGA).
6. Estimated creatinine clearance (for patients > 12 years) greater than 50.0 mL/minute (using the Cockcroft-Gault formula and actual body weight); for pediatric patients (> 1 year to 12 years), Glomerular Filtration Rate (GFR) estimated by the updated Schwartz formula ≥ 90.0 mL/min/1.73 m^2. If the estimated creatinine clearance is < 90 mL/min/1.73 m^2, then renal function must be measured by 24-hour creatinine clearance or nuclear GFR, and must be > 70.0 mL/min/1.73 m^2.
7. Pulmonary function: Diffusing capacity of the lung for carbon monoxide (DLCO) ≥ 50% (adjusted for hemoglobin), and forced expiratory volume in one second (FEV1) or forced vital capacity (FVC) ≥ 50%; for children who are unable to perform for Pulmonary Function Tests (PFTs) due to age or developmental ability, there must be no evidence of dyspnea and no need for supplemental oxygen, as evidenced by O2 saturation ≥ 92% on room air.
8. Liver function: total bilirubin < 2x the upper limit of normal (unless elevated bilirubin is attributed to Gilbert's Syndrome) and alanine aminotransferase (ALT) / aspartate aminotransferase (AST) < 2.5x the upper limit of normal.
9. Signed informed consent.

Exclusion Criteria:

1. Prior autologous or allogeneic hematopoietic stem cell transplant
2. Karnofsky or Lansky Performance Score < 70%
3. Active central nervous system (CNS) involvement by malignant cells
4. Patients with uncontrolled bacterial, viral or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment
5. Presence of fluid collection (ascites, pleural or pericardial effusion) that interferes with methotrexate clearance or makes methotrexate use contraindicated
6. Patients seropositive for HIV-1 or -2
7. Patients seropositive for Human T-Lymphotrophic Virus (HTLV)-I or -II
8. Patients with active Hepatitis B or C viral replication by polymerase chain reaction (PCR)
9. Documented allergy to iron dextran or murine proteins
10. Women who are pregnant (positive serum or urine βHCG) or breastfeeding
11. Females of childbearing potential (FCBP) or men who have sexual contact with FCBP unwilling to use 2 effective forms of birth control or abstinence for one year after transplantation
12. History of uncontrolled autoimmune disease or on active treatment
13. Patients with prior malignancies, except resected non-melanoma or treated cervical carcinoma in situ. Cancer treated with curative intent ≥ 5 years previously will be allowed. Cancer treated with curative intent < 5 years previously will not be allowed unless approved by the Protocol Officer or one of the Protocol Chairs.
14. Patient unable to comply with the treatment protocol including appropriate supportive care, follow-up and research tests
15. Planned post-transplant maintenance therapy except for FLT3 inhibitors or TKIs
16. German centers only: Treatment with any known non-marketed drug substance or experimental therapy within 5 terminal half lives or 4 weeks prior to enrollment, whichever is longer, or participation in any other interventional clinical study.