Did Kobe Bryant play on the best teams of any superstar of his generation?
Did Kevin Garnett play on the worst teams of any superstar of his generation?
Did Jason Kidd's teams fall apart without him?
Did Allen Iverson really help the 76ers that much?
Below are a few cursory bits of data to answer those questions. Using NBA.com data, we now have 16 seasons of on/off (1997-present). Here are the career playoff on/off numbers of the most notable players from that period:

Sorted by just On performance:

Sorted by Off performance:

Obviously, time is a huge variable in this equation as some of these figures span 15 seasons. The best 5-year stretches (5 consecutive postseasons played):

The 5-year stretches are still relatively small samples, although for most players they are more consistent and interesting samples. Most players also had their best on/off stretches in what are often considered the hearts of their prime.
With that said, my general take on this numbers:
(1) Off is interesting, although sample-size is an issue usually
(2) On is really interesting, because regardless of how much a player causes it, we can at least isolate the performance of teams with superstars on the court.