  We observe the decays $ $D^*_{s1}(2710)^+ \to D^*K$ and $D^*_{sJ}(2860)^+ \to D^*K$ and measure their branching fractions relative to the $D K$ final state. We also observe, in the $D^*K$ mass spectrum, a new broad structure at a mass of $(3044 \pm 8_{stat} (^{+30}_{-5})_{syst})$ $MeV/c^2$ having a width $\Gamma=(239 \pm 35_{stat} (^{+46}_{-42})_{syst})$ $MeV$. To obtain this result we use 470 ${\rm fb}^{-1}$ of data recorded by the BaBar detector at the PEPII asymmetric-energy $e^+e^-$ storage rings at the Stanford Linear Accelerator Center running at center-of-mass energies near 10.6 GeV. 
Study of $D_{sJ}$ decays to $D^*K$ in inclusive $e^+e^-$ interactions