  Motivated by the experiments of heavy flavor physics at running LHC and
upgrading SuperKEKB/Belle-II in the future, the nonleptonic $B^{\ast}_{(s)}\to
M_1 M_2$ $(M=D$, $D_s$, $\pi$, $K)$ weak decays are studied in this paper. The
amplitudes are calculated with factorization approach, and the transition form
factors $A_0^{B^{\ast}_{(s)}\to M_1}(0)$ are evaluated within BSW model. With
the reasonable approximation $\Gamma_{tot}(B^*_{(s)})\simeq \Gamma(B^*_{(s)}\to
B_{(s)}\gamma)$, our predictions of branching fractions are presented.
Numerically, the CKM-favored tree-dominated $\bar{B}^{*0} \to D^+D^-_s$ and
$\bar{B}^{*0}_s \to D^+_sD^-_s$ decays have the largest branching fractions of
the order $\sim{\cal O}(10^{-8})$, and hence will be firstly observed by
forthcoming Belle-II experiment. However, most of the other decay modes have
the branching fractions~$<{\cal O}(10^{-9})$ and thus are hardly to be observed
soon. Besides, for the possible detectable $B^{\ast}_{(s)}$ decays with
branching fractions $\gtrsim{\cal O}(10^{-9})$, some useful ratios, such as
$R_D$ {\it et al.,} are presented and discussed in detail.
