  We systematically analyze the supersymmetric contributions to the mixing CP
asymmetries and branching ratios of B -> Phi K(S) and B -> eta(prime) K(S)
processes. We consider both gluino and chargino exchanges in a model
independent way by using the mass insertion approximation method. While we
adopt the QCD factorization approach for evaluating the corresponding hadronic
matrix elements, a critical comparison with predictions in naive factorization
one is also provided. We find that pure chargino contributions cannot
accommodate the current experimental results on CP asymmetries, mainly due to b
-> s gamma constraints. We show that charged Higgs contributions can relax
these constraints making chargino responsible for large asymmetries. On the
other hand, gluino exchanges can easily saturate both the constraints on B ->
Phi K(S) and B -> eta(prime) K(S) CP asymmetries. Moreover, we also find that
the simultaneous contributions from gluino and chargino exchanges could easily
account for the present experimental results on the mentioned asymmetries.
Remarkably, large experimentally allowed enhancements of B -> eta(prime) K(S)
branching ratio can easily be achieved by the contribution of two mass
insertions in gluino exchanges. Finally, we analyze the correlations between
the CP asymmetries of these processes and the direct CP asymmetry in b -> s
gamma decay. When all experimental constraints are satisfied, supersymmetry
favors large and positive values of b -> s gamma asymmetry.
