Hi. I don't have any experience with the higher-quality brakes used on modern road-racing bikes, but here's how what I do, to centralise caliper brakes. It's an old trick I learnt in a bike shop, years ago. A little crude perhaps, but very effective.
You will need three or four items:
A small to medium hammer,
A drift, or pin punch, or a length of 1/4", 6 m/m rod, or similar
Care and Patience.
First ensure that the brake shoes are set correctly against the rims, and that the nut is tight at the mounting. Also adjust
the front to eliminate slack in the arms ( so they don't rock
forward when contacting the rim ). I generally use a 10 m/m socket on the domed nut, and an 11 m/m Park,thin, flat spanner on the adjusting nut.
Now place the drift on the brake spring - on the side of the brake which has the bigger gap - and give it a tap with the hammer. No change? Another tap, a little harder. Oops, moved too far? Tap the spring on the other side to bring it back. Operate the brake lever after each tap, to see where the arms settle. Works fine for me everytime, and stays put for a long time.
Sheldon Brown's website has a wealth of information on brakes, among other things.
I think that the two arms of the one-piece spring have unequal tensions, and thus the brake tends to want to centralise itself accordingly, which is not neccessarily the centre of the forks. This inequality may be caused by minor differences in the heat-treatment of the spring - the quenching, tempering, embrittlement of the spring after electroplating, minor differences in length, etc.
Which also explains why cantilever brakes, and vee brakes, have provision for adjustment - to equalise the tensions of, in this case, two separate springs, in order to centralise the arms in relations to the forks. If you were to measure the valve springs in your car, even new ones, you would find them to be of slightly different lengths, and they would also compress to different heights when loaded with the same weights.
All the above assumes that your brakes are not binding on the
pivot bolt, and that your bosses are clean and greased for your vee brake pivots. And that your (front) wheel fits the centre of the forks no matter which way round the wheel is fitted. i.e., that the wheel was built with the rim centred over the hub, no offset or dish, and having equal spacers each side of the cones.
Cheers.