A Modified Dose of Rabbit Anti-thymocyte Globulin (rATG) in Children and Adults Receiving Treatment to Help Prepare Their Bodies for a Bone Marrow Transplant

Inclusion Criteria: * Patients receiving first peripheral blood mobilized ex-vivo CD34-selected T cell depleted allo-HCT for the following hematologic malignant conditions: * Acute myeloid leukemia (AML) with intermediate or high-risk features in CR1 or Relapse AML in ≥ CR2. * Must have MRD \<5% (flow cytometry, molecular and/or cytogenetics accepted). * Acute leukemias of ambiguous lineage in ≥ CR1. * Must have MRD \<5% (flow cytometry, molecular and/or cytogenetics accepted). * Acute lymphoid leukemia (ALL) in CR1 with clinical, flow cytometric, or molecular features indicating a high risk for relapse, or ALL in ≥ CR2. * Adult Patients - recommended but not required to be MRDnegative (by flow cytometry, molecular and/or cytogenetics). * Pediatric Patients - Must be MRD-negative by flow cytometry, molecular and/or cytogenetics. * Myelodysplastic syndromes (MDS) with least one of the following: * Revised International Prognostic Scoring System risk score of intermediate or higher at the time of transplant evaluation. * Life-threatening cytopenia. * Karyotype or genomic changes that indicate high risk for progression to acute myelogenous leukemia, including abnormalities of chromosome 7 or 3, mutations of TP53, or complex or monosomal karyotype. * Therapy related disease or disease evolving from other malignant processes. * Able to tolerate cytoreduction * Patients age: * Regimen A: 4 - 60 years * Regimen B - no age restriction * Adequate organ function is required, defined as follows: * Hepatic: Serum bilirubin ≤ 2 mg/dL, unless benign congenital hyperbilirubinemia. Patients with hyperbilirubinemia related to paroxysmal nocturnal hemoglobinuria or other hemolytic disorders are eligible with PI approval. * Hepatic: AST, ALT, and alkaline phosphatase \< 2.5 times the upper limit of normal unless thought to be disease-related. * 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 by Age * 1 week 40.6 + / - 14.8 * 2 - 8 weeks 65.8 + / - 24.8 °\> 8 weeks 95.7 +/- 21.7 * 2 - 12 years 133 +/- 27 * 13 - 21 years (males) 140 +/- 30 * 13 - 21 years (females) 126.0 + / - 22.0 * Cardiac: LVEF ≥ 50% by MUGA or resting echocardiogram. * Pulmonary: Pulmonary function testing (FEV1 and corrected DLCO) ≥ 50% predicted (pediatric patients unable to complete PFTs will need oxygen saturation as recorded by pulse oximetry of ≥92% on room air). * Adequate performance status: * Age ≥ 16 years: ECOG ≤ 1 or Karnofsky 70% * Age \< 16 years: Lansky 70% * Each patient must be willing to participate as a research subject and must sign an informed consent form or legal guardian with assent as appropriate. Exclusion Criteria: * Patients with active extramedullary disease. * Patients with active central nervous system malignancy. * Uncontrolled infection at the time of allo-HCT. * Patients who have undergone previous allo-HCT. * Patient seropositivity for HIV I/II and/or HTLV I/II. * Females who are pregnant or breastfeeding. * Patients unwilling to use contraception during the study period. * Patient or parent or guardian unable to give informed consent or unable to comply with the treatment protocol including research tests. Donor Inclusion Criteria: * Related or Unrelated Donors: °8/8 HLA matched at A, B, C, and DRB1 loci, as tested by DNA analysis. * Able to provide informed consent for the donation process per institutional standards. * Meet standard criteria for donor collection (e.g. National Marrow Donor Program Guidelines or collecting center guidelines as approved by treating physician). * Provide GSCF mobilized peripheral blood stem cells