Catalytic P systems is one of the basic classes of P systems. The number of catalysts required for optimal universality results (both in pure catalytic systems and catalytic systems) has been a problem of extensive research ,,,,. The differences that can give universality/non-universality are very small in these systems, and finding this borderline is one of the ‘jewel’ problems in P systems . In this paper, we try to figure out this borderline and have obtained some interesting results. We have proved that with 2 catalysts, if
-rules are not used, then universality cannot be obtained. We also consider two restricted variants of pure catalytic systems and prove that they are also not universal. Finally, we look at mobile catalytic systems and solve two open problems.