Comparison of Triple GVHD Prophylaxis Regimens for Nonmyeloablative or Reduced Intensity Conditioning Unrelated Mobilized Blood Cell Transplantation

Inclusion Criteria: * Ages \> 50 years with hematologic malignancies treatable by unrelated hematopoietic cell transplant (HCT) * Ages 18-50 years with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant * Ages 18-50 years with chronic lymphocytic leukemia (CLL) * Ages 18-50 years with hematologic diseases treatable by allogeneic HCT who refuse a high-dose HCT; transplants must be approved for these inclusion criteria by the principal investigator * The following diseases will be permitted although other diagnoses can be considered if approved by PCC and the principal investigator. * Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as diffuse large B cell NHL- not eligible for autologous HCT, not eligible for high-dose allogeneic HCT, or after failed autologous HCT * Mantle cell NHL - may be treated in first complete remission (CR); (diagnostic lumbar puncture \[LP\] required pre-transplant) * Low grade NHL - with \< 6 month duration of CR between courses of conventional therapy * CLL - must have either 1) failed to meet National Cancer Institute (NCI) Working Group criteria for complete or partial response after therapy with a regimen containing fludarabine (FLU) (or another nucleoside analog, e.g. cladribine \[2-CDA\], pentostatin) or experience disease relapse within 12 months after comple…