Inclusion Criteria:

          -  Patients with recurrent solid tumors

          -  Patients with malignant melanoma

          -  Patients with hematological malignancies.

               -  Chronic myelogenous leukemia in chronic or accelerated phase, to include chronic
                  myelomonocytic leukemia (juvenile chronic myelogenous leukemia (JCML) or CMML).

               -  Acute lymphoblastic leukemia (ALL)

                    -  First remission high-risk ALL (Ph+ with initial high white blood cell (WBC)t
                       (4-11) in infants less than 1 year and CALLA negative)

                    -  Second or subsequent remission ALL or isolated extramedullary disease on or
                       off therapy.

               -  Acute non-lymphocytic leukemia (ANLL)

                    -  Patients with ANLL in first remission who have a matched sibling donor.

                    -  ANLL in second remission, or patients who only achieve an initial partial
                       remission < 15% blasts, or early relapse.

               -  Myelodysplastic syndromes (MDS): refractory anemia (RA), refractory anemia with
                  excess blasts (RAEB), refractory anemia with excess blasts in transformation
                  (RAEB-T) and CMML/JCML.

          -  Selected immunodeficiencies:

               -  Wiskott-Aldrich syndrome.

               -  Severe combined immunodeficiency variants that require ablation.

               -  Hyper-Immunoglobulin M (IgM) syndrome.

               -  Other immune deficiencies after approval from the medical director.

          -  Bone marrow failure syndromes (single or multiple hematopoietic lines)

          -  Venous access: A double lumen central vascular access device or its equivalent will be
             required for all patients entered on the protocol.

          -  Informed consent: The donor and the patient and/or the patient's legally authorized
             guardian must acknowledge in writing that consent to become a study subject has been
             obtained in accordance with the institutional policy approved by the United States
             (U.S.) Department of Health and Human Services.

          -  Patient organ function requirements:

               -  Adequate renal function: serum creatinine < 2 x normal, or creatinine clearance
                  calculated by Schwartz formula, of glomerular filtration rate (GFR) > 40
                  ml/min/1.73m2, or an equivalent GFR as determined by the institutional normal
                  range.

               -  Adequate liver function: total bilirubin </= 2 x normal; and Aspartate
                  aminotransferase (AST) or Alanine aminotransferase (ALT) </= 4 x normal.

               -  Adequate cardiac function: shortening fraction of > 24% by echocardiogram, or
                  ejection fraction of > 30% by radionuclide angiogram.

               -  Adequate pulmonary function: Diffusion Lung Capacity Carbon Monoxide (DLCO),
                  Forced Expiratory Volume in 1 second (FEV1) / Forced Vital Capacity (FVC) > 30%
                  by pulmonary function test. For children who are uncooperative for pulmonary
                  function tests and have no evidence of dyspnea at rest or exercise intolerance,
                  pulse oximetry > 94% on room air is considered acceptable.

               -  Performance status: Lansky Score >/= 60% for children </= 16 years of age; or
                  Karnofsky > 60% status for those > 16 years of age.

        Exclusion Criteria:

          -  Patients who are pregnant

          -  Inability to find a suitable donor for the patient

          -  Patient is HIV-positive

          -  Patient has active Hepatitis B

          -  Disease progression or relapse prior to HPC infusion