The study is multicenter, with six Cord Blood Transplant Centers (CBTCs), two collecting and storage centers (Cord Blood Banks -- CBBs) and one Coordinating Center. Each CBB used the same protocol for recruiting donors, collecting, processing, testing, storage, retrieval from storage, reprocessing from the frozen state, and shipping. Each participating CBTC used the same patient selection criteria, preparative regimen for patients in the same class, initial graft-versus-host disease (GvHD) prophylaxis, indications for the use of cytokines, definitions for events and complications, and methods for evaluating immune reconstitution. The main study evaluated the impact of HLA 3/6 and 4/6 matching on outcome. The primary endpoint was 180-day disease free survival after UCBU transplantation. Secondary endpoints included engraftment, the frequency and severity of acute and chronic GvHD with stratification by degree of HLA match, overall survival, and immunologic reconstitution. Data were collected on banked UCBUs to define unit quality by nucleated cell count and flow cytometry of surface markers to identify effects on patient outcome. Recruitment ended December 31, 2003 with the accrual of 326 subjects. .