A method is disclosed for collecting and processing whole blood. Whole blood is collected at several remote donor sites and transported to a central blood-processing center, where information regarding demand for blood products is used to direct processing of whole blood into blood products. Whole blood is initially collected in collection bags unattached to satellite bags instead of commonly used multiple bag sets. When the determination is made at the blood processing center as to which blood products are to be made, the appropriate satellite bags and/or other system components are sterile docked to the blood-collection bag and the whole blood is processed. The use of blood-collection bags initially unattached to satellite bags eliminates waste and simplifies the transportation and processing of whole blood. Also disclosed are blood collection systems that remove leukocytes and collect whole blood into blood-collection bags unattached to satellite bags.