Inclusion Criteria:

          -  Malignant Disease

               -  Chronic myleogenous leukemia in chronic or accelerated phase

               -  Acute lymphoblastic leukemia (ALL)

                    -  First remission high-risk ALL (Ph+, t( 4-11) infants).

                    -  Second remission ALL, after a short first remission (<36 mos from Dx).

                    -  3rd or greater remission ALL.

               -  Acute myelogenous leukemia (AML)

                    -  First remission high risk acute nonlymphoblastic (ANLL) (as defined by
                       cytogenetics), if a matched sibling donor is available.

                    -  Initial partial remission AML (<20% blasts in the bone marrow).

                    -  AML that is refractory to two cycles of induction therapy.

                    -  Second or greater remission AML

               -  Myelodysplastic/Myeloproliferative Disease

                    -  Juvenile Myelomonocytic Leukemia (JMML)

                    -  Myelosplastic syndrome and/or pre-leukemia at any stage

               -  Lymphoma

                    -  Relapsed lymphoma with residual disease that appears to be chemo-sensitive
                       and non-bulky (<5 cm at largest diameter)

          -  Venous Access: Three lumens of central vascular access will be required for all
             patients entered on protocol due to the need for a dedicated line for continuous
             infusion cyclosporine.

          -  Informed Consent: 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 policies approved by the U.S. Department of Health
             and Human Services.

          -  Patient organ function requirements:

               -  Adequate renal function: Serum Creatinine <~1.5 x normal, or Creatinine clearance
                  of 70 mL/min/1.73 mE2 or an equivalent GFR as determined by the institutional
                  normal range

               -  Adequate liver function: Total bilirubin <1.5 x normal; and SGOT (AST) or SGPT
                  (ALT) <~2.5 x normal

               -  Adequate cardiac function: Shortening fraction of >/=27% by echocardiogram

               -  Adequate pulmonary function: FEV1/FVC >/=60% by pulmonary function test; for
                  children who are uncooperative, no evidence of dysnpea at rest, or exercise
                  intolerance, and must have a pulse oximetry >94% in room air

          -  Performance status: Lansky for children </= 16 years >/= 60; Karnofsky status for
             those > 16 years of age >/= 70

          -  Effective Contraceptive Use: Women of childbearing potential and sexually active males
             should use effective contraception while on study.

        Exclusion Criteria:

          -  Patients who are pregnant or lactating

          -  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