Methods of forming a replacement gate structure for a transistor device

One illustrative IC product disclosed herein includes a transistor device formed on a semiconductor substrate, the transistor device comprising a gate structure comprising an upper surface, a polish-stop sidewall spacer positioned adjacent the gate structure, wherein, at a location above an upper surface of the semiconductor substrate, when viewed in a cross-section taken through the first polish-stop sidewall spacer in a direction corresponding to a gate length direction of the transistor, an upper surface of the gate structure is substantially coplanar with an upper surface of the polish-stop sidewall spacer.