Between compressor and air cleaner, keep the same size as outer comp housing which could easy be 4" or so.. Use silicon hose to join..
This part the size should be big as possible due to no pressure area..
The outlet should be the size of outlet comp and kept small enough to get through engine bay etc.. The at approx 1/3 distance to intercooler [if front mount ?] increase to the size of intercoolers inlet ... Same with pipe from intercooler to throttle body..
Should be same size, a 3" pipe is easy enough for 700+ h.p...
The dump pipe?? Run as big as you can,,, Then if you want ?? Y pipe to Run twin X 3" exhaust. With cat on each side.. You won't loose too much of the V8 sound.. Use mufflers which are straight through, no baffles...
Here's my push rod with twin 3" exhaust, straight through mufflers.. Click on image to hear..
Idle from cold..

Even though turbo quietens things down.. You still don't loose that V8 sound...
Unless you want to...
I used mild steel and had them ceramic coated .. They look like stainless steel and keeps heat away or doesn't radiate heat too much..