Inclusion Criteria:

          -  Appropriate diagnosis: Patients must have a disease or syndrome amenable to therapy
             with hematopoietic stem cell transplantation. Diagnoses include, but are not limited
             to:

          -  Congenital and Other Non-malignant Disorders:

          -  Immunodeficiency disorders (e.g. Severe Combined Immunodeficiency, Wiskott-Aldrich
             Syndrome)

          -  Congenital hematopoietic stem cell defects (e.g. Chediak-Higashi Syndrome, Congenital
             Osteopetrosis, Osteogenesis Imperfecta)

          -  Metabolic disorders (e.g. Hurler's Syndrome)

          -  Severe aplastic anemia

          -  High-Risk Leukemia:

          -  Acute Myelogenous Leukemia

          -  Refractory to standard induction therapy (more than 1 cycle required to achieve
             remission)

               -  Recurrent (in CR ≥ 2)

               -  Treatment-related AML or MDS

               -  Evolved from myelodysplastic syndrome

               -  Presence of FLT3 abnormalities

               -  FAB M6 or M7

               -  Adverse cytogenetics

               -  Myelodysplastic Syndrome

               -  Acute Lymphoblastic Leukemia including T lymphoblastic leukemia:

               -  Refractory to standard induction therapy (time to CR >4 weeks)

               -  Recurrent (in CR ≥ 2)

               -  WBC count >30,000/mcL at diagnosis

               -  Age >30 at diagnosis

          -  Adverse cytogenetics, such as t(9:22), t(1:19), t(4:11), and other MLL rearrangements.

          -  Chronic Myelogenous Leukemia in accelerated phase or blast crisis

          -  Biphenotypic or undifferentiated leukemia

          -  Burkitt's leukemia or lymphoma

          -  Lymphoma:

          -  Large cell, Mantle cell, Hodgkin lymphoma refractory or recurrent, chemo-sensitive,
             and ineligible for an autologous stem cell transplant or previously treated with
             autologous SCT

          -  Marginal zone or follicular lymphoma that is progressive after at least two prior
             therapies

          -  Multiple Myeloma, recurrent following high-dose therapy and autologous SCT or
             ineligible for an autologous HSCT

          -  Solid tumors, with efficacy of allogeneic HSCT demonstrated for the specific disease
             and disease status

          -  Adequate organ function:

          -  Cardiac - LVEF >45%, or shortening fraction >25%, Absence of congestive heart failure
             or conduction disturbances with high risk for sudden death

          -  Pulmonary - DLCO (corrected for hemoglobin), FEV1 and FVC ≥ 50% predicted;

          -  Renal - serum Cr < 1.5 times the upper limit of normal for age or GFR ≥ 50
             ml/min/1.73m2

          -  Hepatic - total bilirubin level < 2 times the upper limit of normal (except for
             patients with Gilbert's syndrome or hemolysis); if the primary disease process is
             causal, this criterion will be reconsidered. ALT, AST, and Alkaline phosphatase ≤ 5
             times upper limit of normal.

          -  Performance Status Karnofsky or Lansky score ≥ 70%.

          -  Informed Consent must be obtained prior to initiating conditioning therapy.

          -  Receipt of viable cord blood product(s), single or dual, must be confirmed with the
             stem cell processing laboratory prior to initiating conditioning therapy.

        Exclusion Criteria:

          -  Availability of 10/10 or 9/10 HLA-matched related or unrelated donor within a
             reasonable timeframe dictated by the clinical urgency of the transplant

          -  Autologous HSCT < 6 months prior to proposed UCB transplant

          -  Pregnant or breast feeding

          -  Current uncontrolled infection

          -  Evidence of HIV infection or positive HIV serology