UNDERSIZED sizing die??????????????

WHY? if you will. would I need/use an undersized sizing die , like say a .45 acp sizing die that is 0.003 small then a normal .45 acp die? TYIA.

If you have a full length size die that produces a smaller than usual OD on a case, this is useful in two circumstances, one is with standard brass producing higher than usual neck tension.  The second is that with thinner-than-usual brass (I have lots of old Remington like this), normal neck tension is achieved.  

For normal brass and soft Lead bullets, this does not work.

NuJudge has it, thin brass, jacketed bullets, maybe for very heavy loads to prevent heads from backing out?

I use an undersize die for 9mm range brass. It is useful for brass that may have been shot in a loose chamber. In my application, it allows for correct tension on the projectile.