The study is designed as a Phase III, randomized, open label, multicenter, prospective, comparative trial of granulocyte colony stimulating factor (G-CSF)-mobilized peripheral blood stem cells (PBSC) versus marrow from unrelated donors for transplantation in patients with hematologic malignancies. Recipients will be stratified by transplant center and disease risk and will be randomized to either the PBSC or marrow arm in a 1:1 ratio.