Hematopoietic cell transplants (HCT)are one treatment option for people with leukemia or
lymphoma. Family members,unrelated donors or banked umbilical cordblood units with similar
tissue type can be used for HCT. This study will compare the effectiveness of two new types
of bone marrow transplants in people with leukemia or lymphoma: one that uses bone marrow
donated from family members with only partially matched bone marrow; and, one that uses two
partially matched cord blood units.