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 Donors:  °8/8 or 7/8 HLA matched at A, B, C, and DRB1 loci, as tested by DNA analysis.  Unrelated Donors:  °8/8 or 7/8 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