Measurement of the exclusive branching fractions B⁰ --> eta K^{*0) and B^+ --> eta K^(*+)

We present the results of searches for B decays to the two charmless two-body final states B^0 --> eta K^{*0} and B^+ --> eta K^{*+}, based on 20.7 fb-1 of data collected in 1999 and 2000 with the BABAR detector at PEP-II. We find the branching fractions BF(B^0 --> eta K^{*0}) = (19.8^{+6.5}_{-5.6} +/- 1.7) x 10^{-6} and BF(B^+ --> eta K^{*+}) = (22.1^{+11.1}_{-9.2} +/- 3.3) x 10^{-6}, where the first error quoted is the statistical and the second systematic.