This sounds like the classic AOS (air oil separator) problem, especially if you're getting smoke.
I was getting major hesitation when pressing on the accelerator, but didn't get the standard tell-tale signs of smoke. With the engine running at idle, the hesitation was there (when revving). I then pulled off the oil filler cap (thereby allowing air into the crankcase) and tried again. The hesitation was gone.
I replaced the AOS and the hesitation is gone.
Oh, .... 2002 Boxster, 165,000 exhilarating miles!
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