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