A bottom part of a positive-displacement pipetting system), including a body slideably housing a device for gripping a piston belonging to a capillary-piston assembly the capillary of which is adapted to be fitted onto an end-fitting of the body. The system also comprises means for ejecting the capillary-piston assembly arranged externally with respect to the body. The system is constructed so that a relative rotation between the ejection means and the gripping device causes it to pass from an open configuration enabling the piston to be released to a closed configuration enabling said piston to be retained, and/or the reverse.