CD34+Selection for Partially Matched Family or Matched Unrelated Adult Donor Transplant

Inclusion Criteria: * Adequate renal function defined as:Serum creatinine \<1.5 x normal, or Creatinine clearance or radioisotope GFR \>60 ml/min/m2 or an equivalent GFR as determined by the institutional normal range. * Adequate liver function defined as:Total bilirubin \<1.5 x normal, or SGOT (AST) or SGPT (ALT) \<3.0 x normal * Adequate cardiac function defined as:Shortening fraction \>27% by echocardiogram, or Ejection fraction of \>47% by radionucleotide angiogram or echocardiogram. * Adequate pulmonary function defined as:Uncorrected DLCO \>50% by pulmonary function test. For children who are uncooperative, no evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \>94% on room air. Eligibility for Reduced Intensity Regimen: * Adequate renal function defined as:Serum creatinine 2.0 x normal, or creatinine clearance or radioisotope GFR \> 40 ml/min/m2 or an equivalent GFR as determined by the institutional normal range. * Adequate liver function defined as:Total bilirubin \< 2.5 x normal; or SGOT (AST) or SGPT (ALT) \< 5.0 x normal. * Adequate cardiac function defined as:Shortening fraction of \>25% by echocardiogram, or Ejection fraction of \>40% by radionuclide angiogram or echocardiogram. * Adequate pulmonary function defined as:DLCO \>35% by pulmonary function test. For children who are uncooperative, no evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \>94% in room air. Exclusion Criteria: * Pregnancy/Breast Feeding: Females who are pregnant or breast-feeding are not eligible. * Infection: Patients with documented uncontrolled infection at the time of study entry are not eligible.