Hematopoietic progenitor cell (HPC- primitive cells in the blood, bone marrow and umbilical cord that can restore the bone marrow) transplant can be a curative therapy for the treatment of hematologic malignancies (a disease of the bone marrow and lymph nodes). The source of cells used for the transplant comes from related (sibling) and in cases where there is no sibling match, from unrelated donors through the National Marrow Donor Program.

The availability of a suitable donor can be a significant obstacle for patients who need a transplant but do not have a matched donor. Cord blood that has been harvested from an umbilical cord shortly after birth has a rich supply of cells needed for transplant. These stored cord bloods are now being used to transplant adults without a matched donor.

Advantages to using cord blood includes a readily available source of cells with no risk to the donor during the collection process, immediate source of cells in urgent situations (no lengthy donor work-up)and a reduction in infectious disease transmission to the recipient.

One of the main disadvantages is the cord blood has a small number of cells needed for transplant. In an adult, usually two cords are needed and large recipients do not qualify because they need too many cells.

This study will use two different preparative regimens (chemotherapy and radiation) followed by one or two umbilical cord units (UBC). The preparative regimen used will be chosen by the physician and is based on patient's age, disease and medical condition at the time of transplant.

Multiple objectives for this study include disease-free and overall survival, treatment related mortality, rate of cells taking hold, and the incidence and severity of the transplant complication called graft versus host disease (GVHD).