Drill bits and tools for subterranean drilling, methods of manufacturing such drill bits and tools and methods of directional and off center drilling

A drill bit for subterranean drilling comprising:

• a bit body including a plurality of blades, at least one blade of the plurality of blades extending at least partially over a cone region of the bit body;
• a plurality of cutting structures mounted to the at least one blade;
• a rubbing zone on the surface of the at least one blade within the cone region of the at least one blade, the rubbing zone positioned and configured to effectively rub against a formation being drilled and provide depth-of-cut control, and wherein cutting structures of the plurality of cutting structures substantially within the rubbing zone have a reduced average exposure relative to other cutting structures of the plurality of cutting structures within the cone region, wherein the bit body and the plurality of cutting structures are configured such that a cutter profile of the drill bit extends from a gage region of the at least one blade of the drill bit to a center axis of the drill bit and includes a concavity within the rubbing zone of the at least one blade radially extending greater than a width of any single cutting structure;
• and
• a protrusion within the rubbing zone, the protrusion separate and distinct from the plurality of cutting structures defining the cutter profile and radially extending greater than a width of at least two cutting structures of the plurality of cutting structures defining the cutter profile.