Inclusion Criteria:

- Age 0 (newborn) - 21 years

- Patient must have a malignant or non-malignant disease that can benefit from
alternative stem cell transplantation according to standard practice guidelines.

- Patients with lymphoma or acute leukemia (except acute myeloid leukemia, AML) must be
in remission at the time of transplant.

- Patients must lack a healthy human leukocyte antigen (HLA)-identical related donor.

- Recipient or authorized guardian must sign informed consent for this study.

- If recipient is female and of child-bearing age, negative pregnancy test.

- Patient must have a healthy, willing mismatched related or an unrelated donor who is:

- Able to receive granulocyte colony-stimulating factor (G-CSF) and undergo
apheresis either through placement of catheters in antecubital veins or a
temporary central venous catheter,

- For Related donor: sibling, half-sibling, parent, cousin, aunt, uncle or
grandparent will all be considered eligible.

- For Related donor: HLA antigen genotypic match ≥ 4/8 and ≤ 7/8
(haplocompatible).

- For unrelated donor: 6/8 or 7/8 HLA antigen match (if two mismatches, they must
be at different loci).

- Complete medical history, physical and screening for infectious diseases that
are acceptable for donation.

- If donor is female and of child-bearing age, negative pregnancy test.

- Absence of anti-HLA antibodies in recipient directed against donor antigens.

- Donor must be willing to sign informed consent for this study. If donor is < 18
years of age, donor must be willing to give assent and parents willing to sign
informed consent. For unrelated donors: The National Marrow Donor Program (NMDP)
will obtain informed consent for donor's apheresis product to be used in this
study.

- Age ≥ 11 years

Exclusion Criteria:

- Patient with an anticipated life expectancy of < 1 month

- Active infectious hepatitis or cytomegalovirus (CMV) disease (organ involvement)

- Human immunodeficiency virus (HIV) or Human T-lymphotropic virus (HTLV-I/II)
infection

- Cardiac ejection fraction < 45%; can be lower if patient is not in clinical cardiac
failure and a reduced intensity conditioning regimen is used.

- Creatinine clearance <60 ml/min/1.72 m2; can be lower if a reduced intensity
conditioning regimen is used.

- Pulmonary diffusion capacity (corrected for hemoglobin), forced expiratory volume in
one second (FEV1), or forced vital capacity (FVC) <60% of predicted or oxygen
saturation (O2 sat) > 94% on room air if unable to perform pulmonary function tests
(PFTs); can be lower if a reduced intensity conditioning regimen is used.

- Serum alanine aminotransferase (ALT) > 5 x upper limit of normal (can be up to 10x
upper limit of normal if a reduced intensity conditioning regimen is used) or
bilirubin > 2.

- Performance score (Lansky/Karnofsky) < 50

- Any condition that compromises compliance with the procedures of this protocol, as
judged by the principal investigator.