Does anyone have any good links to the underlying engineering-math of various turbo systems on the market and why the components are designed and sized as they are?

 

There are a couple of really good books, but the shorter answer is using the compressor map to size the cold side of the turbo to the power of the engine without boost, and with the desired power increase. Hot side sizing is an effort to balance flow against quick spool-up. But you don't always need, or want, spooling at low RPM.
Anyway, for the hot side you check with what results others are having on similar-displacement engines to see what spools at what RPM. A smaller-number A/R spools quick but limits power.
For the compressor map, if you have a 300 HP engine, it uses 30 lbs of air per minute. At 2 bar, or 14.7 psi of boost, it will need 60 lb/min. Then you want to keep that above 70% efficiency on the map. That's the simplified version. And better than you're going to get for the $200 GT45 copies off EBay.

 

Exactly the kind of answer I was hoping for!! Thanks much Steven. That gives me a ton to chew on.

 

Read: Maximum Boost by Corky Bell. It's old, but will get you started.

 

Turbo Real World High Performance Turbocharger Systems I found to be a complete book. Covers everything from mapping your turbo to rebuilding turbos. Suggestions on building a turbo engine to tuning it. List several manufacturer's turbos with maps.