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We report a measurement of the time-dependent CP asymmetry of B[over ¯]^{0}→D_{CP}^{(*)}h^{0} decays, where the light neutral hadron h^{0} is a π^{0}, η, or ω meson, and the neutral D meson is reconstructed in the CP eigenstates K^{+}K^{-}, K_{S}^{0}π^{0}, or K_{S}^{0}ω. The measurement is performed combining the final data samples …