Measurements of the Branching Fractions of B0 --> K^*0K+K-, B0 --> K^*0pi+K-, B0 --> K*0K+pi-, and B0 --> K*0pi+pi-

Branching fraction and asymmetry measurements of charmless $B^0\to K^{*0}h^+_1h^-2$($h{1,2}$=$K$,$\pi$) decays are presented, using a data sample of 383 million $\mathrm{{\rm Y}}(4S)\to$ B\bar{B} decays collected with the BaBar detector at the PEP-II asymmetric-energy $B$-meson factory at SLAC. The results are: $\mathcal{B}$($B^0\to K^{\ast 0}{K}^{+}{K}^{-})$ = (27.5 $\pm$ 1.3 $\pm$ 2.2) $\times$ 10${}^{-6}$, $\mathcal{B}$($B^0$ $\to$ $K^{\ast 0}{\pi }^{+}{K}^{-}$) = (4.6 $\pm$ 1.1 $\pm$ 0.8) $\times$ 10${}^{-6}$ and $\mathcal{B}$($B^0$ $\to$ $K^{\ast 0}{\pi }^{+}{\pi }^{-}$) = (54.5 $\pm$ 2.9 $\pm$ 4.3) $\times$ 10${}^{-6}$. The first errors quoted are statistical and the second are systematic. An upper limit is set for ${\cal B}$($B^0$ $\to$ $K^{\ast 0}{K}^{+}{\pi }^{-}$) $<$ 2.2 $\times$ 10${}^{-6}$ at 90% confidence level. We also present measurements of CP-violating asymmetries for the observed decays.