The present invention relates to methods and compositions for providing hematopoietic function in immunodeficient human patients, by selecting an expanded human umbilical cord blood stem/progenitor cell sample without taking into account the HLA-type of the expanded human cord blood stem/progenitor sample or the HLA-type of the patient and administering the selected expanded human cord blood stem/progenitor cell sample to the patient. Methods for obtaining the expanded human cord blood stem/progenitor cell samples, banks of frozen expanded human cord blood stem/progenitor cell samples, and methods for producing such banks are also provided herein.
