  A program of measuring the light hadrons production in exclusive $e^+e^-$ to
hadrons processes is in place at BaBar with the aim to improve the calculation
of the hadronic contribution to the muon $g-2$. We present the most recent
results obtained by using the full data set of about $514 \mathrm{fb}^{-1}$
collected by the BaBar experiment at the PEP-II $e^+e^-$ collider at a
center-of-mass energy of about $10.6$ GeV. In particular, we report the results
on the channels $e^+e^-\rightarrow \pi^+ \pi^- 3\pi^0$, $e^+e^-\rightarrow
\pi^+\pi^- 2\pi^0\eta$, and its resonant sub-states. These final states are
studied in a wide mass range,from threshold production up to about $4 GeV/c^2$.
In addition to the cross-sections, twelve $J/\psi$ and $\psi(2S)$ branching
fractions were measured with ten of them be a first-time measurement.
