Methods of forming replacement gate structures on transistor devices

A method, comprising:

• forming a continuous line-type sacrificial gate structure above a semiconductor substrate by performing a method that comprises:
• forming a sacrificial gate insulation layer above said semiconductor substrate;
• forming a first sacrificial gate electrode material layer above said sacrificial gate insulation layer;
• and
• forming a second sacrificial gate electrode material layer above said first sacrificial gate electrode material layer;
• after forming said continuous line-type sacrificial gate structure, removing a portion of said second sacrificial gate electrode material layer and removing a portion of said first sacrificial gate electrode material layer so as to thereby form a first opening positioned above said sacrificial gate insulation layer, wherein said first opening extends through an entirety of said second sacrificial gate electrode material layer of said continuous line-type sacrificial gate structure and at least partially through said first sacrificial gate electrode material layer of said continuous line-type sacrificial gate structure;
• forming an insulating gate separation structure in said first opening;
• removing materials of said sacrificial gate structure on opposite sides of said insulating gate separation structure to form first and second replacement gate cavities on said opposite sides of said insulating gate separation structure;
• and
• forming first and second replacement gate structures in said first and second replacement gate cavities, respectively.