  We report on preliminary results of searches for penguin mediated B decays
based on 20.7 fb^{-1} of data collected at the Y(4S) peak with the BABAR
detector at PEP-II. The following branching fractions have been measured: BR(B+
--> phi K+) = (7.7^{+1.6}_{-1.4} +- 0.8)*10^{-6}, BR(B0 --> phi K0) =
(8.1^{+3.1}_{-2.5} +- 0.8)*10^{-6}, BR(B+ --> phi K*+) = (9.7^{+4.2}_{-3.4} +-
1.7)*10^{-6}, BR(B0 --> phi K*0) = (8.7^{+2.5}_{-2.1} +- 1.1)*10^{-6}, BR(B+-->
omega pi+) = (6.6^{+2.1}_{-1.8} +- 0.7)*10^{-6}, BR(B --> eta K^*0) =
(19.8^{+6.5}_{-5.6} +-1.7)*10^{-6}, where the first error is statistical and
the second systematic. For several other modes we report upper limits on their
branching fractions; for example for the following flavor-changing neutral
current decays, BR(B--> K l+ l-) < 0.6*10^{-6}, BR(B--> K* l+ l-) <
2.5*10^{-6}, at 90% Confidence Level (C.L.).
