(a) the brake pressure equals the maximum brake pressure, or
(b) the tires start skidding.
(a) not true, under extreme hard braking there are small particles of metal embedded into the compound which get hot and "weld" themselves to the brake disc, this forms a mechanical bond which has to be physically broken rather than just relying on friction.
The friction of Carbon Carbon brakes increases as they get hotter, so for the same brake pressure as they heat up they get grippier.
(b) not true, Depending on the Mu and the surface texture the maximum retardation is just before the skid onset.