Unrelated Cord Blood Transplant Plus a Haplo-Identical (Half-Matched), T-Cell Depleted Stem Transplant From a Related Donor for Subjects With High Risk Malignancies

Inclusion Criteria:

* Patient Selection Criteria: Patients with high risk or refractory malignancies, myelodysplasia (MDS) or severe aplastic anemia amenable to stem cell transplantation therapy but lacking conventional related or unrelated donors will be eligible for this trial.
* Have a consenting related haplo-identical (3/6 or 4/6) stem cell donor;
* Have an available 3, 4, 5, or 6/6 antigen matching unrelated UCB unit that will deliver a cell dose between 2.0-5.0 x 10e7cells/kg.
* Not have a consenting 6/6 or 5/6 antigen matched related bone marrow donor or genetically matched unrelated BM or adult stem cell donor.
* Patients must be \<55 years of age at the time of study enrollment.
* Patients must have histologically confirmed diagnosis of a hematologic malignancy, MDS or severe aplastic anemia. Eligible patients include the following:
* Patients with high risk ALL in first complete remission, with high risk being defined by the presence of hypodiploidy, t(4;11; MLL. 11q23) or t(9;22), or patients presenting with extreme hyperleukocytosis (initial WBC \>500,000/ml) or failure to achieve a complete remission after standard induction therapy.
* All patients with ALL or ANLL in second or subsequent remission.
* Patients with ALL or ANLL in relapse.
* Patients with MDS.
* Patients with CML in any chronic phase, accelerated phase or blast crisis.
* Patients with severe aplastic anemia refractory to medical therapy.
* Patients must not have active CNS disease at the time of study enrollment.
* Patients must have a good performance status (Lansky 80-100%, Karnofsky 50-100%).
* Patients must have adequate function of other organ systems as measured by:
* Creatinine \< 2.0 mg/dl and creatinine clearance \> 50 cc/min/m2.
* Hepatic transaminases (ALT/AST) \< 4 x normal, bilirubin \< 2.0 mg/dl.
* Normal cardiac function by echocardiogram or radionuclide scan, (ejection fraction or shortening fraction \> 80% of normal value for age).
* Pulmonary function tests demonstrating FVC and FEV1 of \>60% of predicted for age. For adult patients DLCO \> 60% of predicted. If patient cannot perform PFTs, clearance by the pediatric or adult pulmonologist will be required.
* Patients must not have uncontrolled infections at the time of cytoreduction.
* Patient, parent, or legal guardian must have given written informed consent according to FDA guidelines.
* Patients may not be pregnant or lactating and must have a current negative pregnancy test.
* Patients must have a minimum life expectancy of at least 3 months.
* Patients must have an available related haplo-identical stem cell donor and an available unrelated cord blood donor delivering between 2 x10e7 cells/kg and 5 x 10e7 cells/kg and matching at a minimum of 3/6 HLA loci.
* Patients must be HIV negative.
* Patients must not be concurrently involved in any other clinical trial that affects engraftment or immune reconstitution (e.g. other hematopoietic growth factors).
* Patients must not have any co-morbid condition which, in the view of the Principal Investigators, renders the patient at too high a risk from treatment complications and regimen related morbidity/mortality.