Fluid separation chambers are provided for rotation about an axis in a fluid processing system. The fluid separation chamber may be provided with first and second stages, with the first and second stages being positioned at different axial locations. In another embodiment, at least one of the stages may be provided with a non-uniform outer diameter about the rotational axis, which may define a generally spiral-shaped profile or a different profile for fractionating a fluid or fluid component. One or more of the stages may also have a varying outer diameter along the axis. The profile of the chamber may be provided by the chamber itself (in the case of rigid chambers) or by an associated fixture or centrifuge apparatus (in the case of flexible chambers).