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We calculate the $B_c\\to B_{sJ}$ and $B_c\\to B_{J}$ form factors within the covariant light-front quark model, where the $B_{sJ}$ and $B_{J}$ denote an s-wave or p-wave $\\bar bs$ and $\\bar bd$ meson, respectively. The form factors at $q^2=0$ are directly computed while their $q^2$-distributions are obtained by the extrapolation. The derived form factors are then used to study semileptonic $B_c\\to (B_{sJ},B_{J})\\bar\\ell\\nu$ decays, and nonleptonic $B_c\\to B_{sJ}\\pi$. 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