Charmless Three-body $B$ Decays at BABAR

We present Dalitz-plot analyses of $B^+\to K^+\pi^-\pi^+$ and $B^0\to K^+\pi^-\pi^0$ using the data sample collected at the $\Upsilon(4S)$ by the BABAR detector. We have found evidence for direct CP-violation in the decay $B^\pm\to\rho^0 K^\pm$, with a CP-violation parameter ${\cal A}_{CP}={\Gamma_{B^+}-\Gamma_{B^-}\over \Gamma_{B^+}+\Gamma_{B^-}}= (+44\pm10\pm4^{+5}_{-13})$, where $\Gamma_{B^\pm}$ are the decay rates. The uncertainties are statistical, systematic, and model-dependent, respectively. We also search for the suppressed decays $B^+\to K^-\pi^+\pi^+$ and $K^+K^+\pi^-$ and improve upper limits on the decay branching fractions.