Allogeneic Transplantation for Pediatric Leukemias With Unrelated Donors

Inclusion Criteria: * Ages 0-21 * AML in one of the following stages: * Having preceding myelodysplasia (MDS) * High Risk cytogenetics * Requiring \> 2 cycles chemotherapy to obtain complete remission * High allelic ratio FLT3/ITD+, * Standard risk cytogenetics with positive MRD at end of Induction * Second or greater CR * First relapse with \< 25% blasts in bone marrow * With therapy-related AML whose prior malignancy has been in remission for at least 12 months * ALL in one of the following stages: * High risk first remission, defined as: * Ph+ ALL; or, * MLL rearrangement with slow early response \[defined as having M2 (5-25% blasts) or M3 (\>25% blasts on bone marrow examination on Day 14 of induction therapy)\]; or, * Hypodiploidy (\< 44 chromosomes or DNA index \< 0.81); or, * End of induction M3 bone marrow; or, * End of induction M2 marrow or MRD\>1% with M2-3 marrow or MRD\>1% at Day 42. * High-risk infant ALL defined as age \<6 months at diagnosis with MLL (11q23) translocation. * High risk second remission, defined as: * Bone marrow relapse \< 36 months from induction; or \>36 mths if a matched sibling donor is available * T-lineage relapse at any time; or, * Very early isolated CNS relapse (\<18 months from diagnosis); or, * Slow reinduction (M2-3 at Day 28) after relapse at any time. * Any third or subsequent CR. * Biphenotypic or undifferentiated leukemia in any CR or if in first relapse must have \< 25% blasts in bone marrow * MDS at any stage; prior therapies allowed * CML in chronic or accelerated phase; prior therapies allowed * Patient also must have the following organ requirements: * Adequate renal function defined as serum creatinine \<2x normal, or creatinine clearance \> 40 ml/min/m\^2 or 70 ml/min. * Adequate liver function as defined by total bilirubin less than or equal to 2 times normal and AST and ALT less than or equal to 4 times normal. * Adequate cardiac function as defined by: shortening fraction \> 24% by echocardiogram, or ejection fraction \> 30% by radionuclide angiogram. * Adequate pulmonary function as defined by DLCO, FEV1/FVC \> 60% by pulmonary function tests. For children who are uncooperative for PFTs and have no evidence of dyspnea at rest or exercise intolerance, pulse oximetry \> 94% on room air is considered acceptable, with a normal chest xray. * Adequate venous access; a double lumen central vascular access device or its equivalent and an additional PICC line will be required for all patients. * Women of childbearing potential and sexually active males should use effective contraception while on study. Exclusion Criteria: * Inability to give informed consent or assent * Inability to obtain a suitable donor * Patient who is HIV-positive * Patient who has active Hepatitis B * Patient who is pregnant * Patient who is otherwise considered unsuitable for transplant at the discretion of the principal investigator.