The present invention relates to methods and compositions for providing hematopoietic function to human patients in need thereof, by selecting a pool of expanded human cord blood stem/progenitor cell samples for administration to the patient, wherein the samples in the pool collectively do not mismatch the patient at more than 2 of the HLA antigens or alleles typed in the patient； and administering the selected pool of expanded human cord blood stem/progenitor cell samples to the patient. Methods for obtaining the pools of expanded human cord blood stem/progenitor cell samples, banks of frozen pools of expanded human umbilical cord blood stem/progenitor cell samples, and methods for producing such banks are also provided herein.
