We present an analysis of the process $e^+e^- \to \pi^+\pi^-\pi^0$ performed at BABAR using the initial-state radiation (ISR) technique. The analysis is based on the full BABAR data set of 469 fb$^{-1}$, recorded at and near the $\Upsilon$(4S) resonance. From the fit to the measured $3\pi$ mass spectrum we determine the products

$\Gamma(V\to e^+e^-){\cal{B}}(V\to 3\pi)$, where $V$ is the $\omega(780)$ or the $\phi(1020)$ resonance, and ${\cal{B}}(\rho\to 3\pi)$.

The latter isospin-breaking decay is observed with $6\sigma$ significance. The $e^+e^- \to \pi^+\pi^-\pi^0$ cross section is measured from 0.62 to 3.5 GeV with unprecedented precision. The measured cross section is used to calculate the leading-order hadronic contribution to the muon magnetic anomaly from this exclusive final state with improved accuracy.

We also present preliminary results on a study, performed on the same data set,

of the $K^+K^-\pi^+\pi^-\pi^0$, $K_S K^\pm \pi^\mp\pi^0\pi^0$ and $K_SK^\pm \pi^\mp\pi^+pi^-$ final states produced in $e^+e^-$ collisions via ISR.