Geoff,
Firstly, bpaggi (if he is who we think he is) should know, and I would bow to his superior knowledge; it is nice having someone who is at the sharp end of Flight Testing prepared to confirm/refute such statements. Like 212man - I would like to qualify my statements, as he does, by stating that I have no intimate knowledge of the AW139 performance.
Category B performance consists of the provision of AEO data - one of which elements is the provision of "the horizontal distance required to take-off and climb over a 15 m (50-foot) obstacle"; one of the conditions of that manoeuvre is that "a landing can be made safely at any point along the flight path if an engine fails" - which we can assume to mean that the trajectory remains outside the HV diagram. As this is conducted at AEO, we can assume that the most efficient condition of rotor-speed is used (in your text 100%) - no failure is assumed.
Category A - for all of the noise we make about it - is mostly about distances. Under normal circumstances, we can assume that distances are critical only if the engine fails at the critical point - which is at TDP (minus the pilot recognition and intervention time - i.e. one second unless otherwise justified and accepted). The distances are: the rejected distance; and the take-off distance. These distances are specified with one-engine-inoperative.
In meeting the requirement for the rejected distance, the point in space at which the engine-failure is assumed to occur plays its part. TDP is the last point at which the pilot has to be able reject the take off and land; field-of-view and the (average pilot's) ability to fly the helicopter into the area provided by the rejected take-off distance available dictates where this point can be in a vertical and horizontal sense.
For the take-off distance; the pilot must, with a failure recognised at the critical point, be able conduct a contined take-off and avoid all obstacles in achieving the the projected take-off distance required at the appropriate conditions. The achievement of this distance also depends on the point in space of the TDP.
However, as procedures have become more sophisticated, the total energy package has had to be considered; in that package are a number of potential benefits (mainly for the continued take-off - for the rejected take-off, some of these could, if exceeded, be disbenefits): the vertical acceleration at the point of failure; the potential energy contained at the height of the TDP; and the energy stored in the rotor before it is drooped (to the manufacturers recommended setting).
As you well know, this total energy package is used extremely effectively in achieving the OEI trajectory to avoid the take-off surface; in an elevated procedure, it provides the deck-edge miss and utilises the drop down to recover the rotor speed (to 100%?) and provide acceleration to Vtoss.
Now to return to the initial point; the conditions for the Cat A procedure are optimised to utilise all engergy at a single critical point of failure. If that point is passed with all-engines-operating, the procedure ceases to be critical unless (and I can't imagine why this would be the case), the single engine profile is flown with AEO.
Jim