As I understand it the Boost controller does as described. (Happy to be proved wrong though) Lets say we are at 4000ft we select +4lbs of boost with the throttle. So the throttle might be in say the 75% physical position. As we climb the throttle remains physically fixed but the boost controller maintains the boost (By varying the supercharger valves) up to that particular Boost Full throttle height. The Automatic Boost Control (ABC) has 2 functions Overboost protection and Pilot work load alleviation by holding boost constant (within limits) as the pilot climbs or descends.
In say an Allison without a Boost control you do the same say at 4000feet you select +4Lbs Boost (about 23"MAP). You then start to climb unless. If you leave the throttle where it is then MAP/Boost will start to drop so as you climb you need to advance the throttle to maintain your selected boost. In addition an aggressive push ion the throttle could exceed Boost/MAP limits.
If you can get a copy of the RAF manual AP2095 Pilots Notes general it is well described there. Below is a snippet from that manual dealing with the differences between ABC equipped and non ABC equipped aircraft. tHe first paragraph talks about Boost maintenance in the climb
