The draw-in collet is the most common and also the most accurate for holding concentricity. To close the collet, it is drawn into spindle angle. The only moving part (other than the collet) is the draw tube.
Concentricity depends on the accuracy of the spindle and the collet. The order hole of the collet must run concentric with its head angle and back bearing which also must be concentric with each other. There are no other factors involved.