A knee arthroplasty prosthesis includes a femoral component having multiple pieces with engagement means provided for engaging various pieces of the femoral component to one another following their insertion in the incised area of the femur. A tibial component includes multiple pieces designed for assembly following positioning in the incision. The tibial component includes a Morse taper cavity on one piece of the tibial component and a Morse taper extension on another member of the component for receipt therein.