An automated system for lapping thin film magnetic heads comprises a lapping fixture (52) positioned in apposition to a rotary lapping plate (54). A ceramic bar (12), on which the magnetic heads (20) are deposited and from which air bearing head sliders are fabricated, is attached to an adjustable transfer tool (10) that is secured to a bow yoke holder (24). The holder (24) is fixed securely on the lapping fixture (52) so that the air bearing surface of the magnetic heads face the surface of the lapping plate (54). During the lapping process, digital data signals are obtained representative of throat height levels of selected heads (20) spaced along the bar (12). The signals are calibrated and processed by a computer (78) which provides command signals for varying lapping pressure, changing direction of row bow, shifting a weight to achieve proportional lapping along the bar, changing the lapping process to a fine polishing step and forming tapers on the rails of the head sliders.