Inclusion Criteria:

- Patients on this trial will receive two partially HLA matched umbilical cord blood
(UCB) units, if available (treatment arm 1). If two units are not available, then
single UCB unit transplantation will be allowed (on treatment arm 2).

- UCB units will be selected according to the University Of Minnesota UCB Graft
Selection Algorithm. The unrelated cord blood donor(s) must be 4-6/6 HLA-A, B, DRB1
matched with the recipient (HLA matching using molecular techniques: A and B to
antigen level resolution and DR to allele level resolution).

- Patients aged ≤ 2 years at diagnosis (not age of transplant) with hematological
malignancy as detailed below:

- Acute myeloid leukemia: high risk CR1 as evidenced by:

- High risk cytogenetics t(4;11) or other MLL rearrangements; chromosome 5,
7, or 19 abnormalities; complex karyotype (>5 distinct changes); ≥ 2 cycles
to obtain complete response (CR); CR2 or higher; Preceding myelodysplastic
syndrome (MDS); All patients must be in CR or early relapse (i.e., <15%
blasts in BM).

- Acute lymphocytic leukemia: high risk CR1 as evidenced by: High-risk
cytogenetic: t(4;11) or other MLL rearrangements; hypodiploid; t(9;22); >1
cycle to obtain CR; CR2 or higher; All patients must be in CR as defined by
hematological recovery, AND <5% blasts by light microscopy within the bone
marrow with a cellularity of ≥15%.

- Myelodysplasia (MDS) IPSS Int-2 or High risk (i.e. RAEB, RAEBt) or refractory
anemia with severe pancytopenia or high risk cytogenetics. Blasts must be < 10%
by a representative bone marrow aspirate morphology.

- Minimal Residual Disease (MRD): Patients with evidence of minimal residual
disease at the completion of therapy or evidence of rising MRD while on therapy.
MRD will be defined by either flow cytometry (>0.1% residual cells in the blast
gate with immune phenotype of original leukemic clone), by molecular techniques
(PCR or FISH) or conventional cytogenetics (g-banding).

- Recipients must have a Lansky score > or = 50% and have acceptable organ function
defined as:

- Renal: glomerial filtration rate > 60ml/min/1.73m^2

- Hepatic: bilirubin, AST/ALT, ALP < 5 x upper limit of normal,

- Pulmonary function: oxygen saturation >92%

- Cardiac: left ventricular ejection fraction > 45%.

- Voluntary written informed consent before performance of any study-related procedure
not part of normal medical care.

Exclusion Criteria:

- Active infection at time of transplantation (including active infection with
Aspergillus or other mold within 30 days).

- History of HIV infection

- Prior myeloablative transplant within the last 6 months.

- Evidence of active extramedullary disease (including central nervous system
leukemia).