An apparatus for separating whole blood includes a continuous flow separation device in which drawn whole blood is separated into a first and second blood component. The separation device has an inlet for introducing whole blood into the separation device, a first blood component outlet for withdrawing the first blood component, and a second blood component outlet for withdrawing the second blood component. The apparatus also includes a first blood component storage container connected to the first blood component outlet, and a first blood component pump to draw the first blood component from the separation device. Additionally, the apparatus can have second blood component storage container connected to the second blood component outlet, and a controller for controlling fluid flow through the apparatus. The controller monitors the total volume of whole blood drawn from the source, and stops a draw pump when the target whole blood volume is withdrawn.