  We reanalyzed nonleptonic charmless two-body B decays involving tensor mesons
in final state motivated by the disagreement between current experimental
information and theoretical predictions obtained in ISGW2 model for some
$\mathcal{B}(B \to P(V)T)$ (where $P$, $V$ and $T$ denote a pseudoscalar, a
vector and a tensor meson, respectively). We have calculated branching ratios
of charmless $B \to PT$ and $B\to VT$ modes, using $B \to T$ form factors
obtained in the covariant light-front (CLF) approach and the full effective
Hamiltonian. We have considered the $\eta-\eta^{\prime}$ two-mixing angle
formalism for $B \to \eta^{(\prime)}T$ channels, which increases branching
ratios for these processes. Our predictions obtained in the CLF approach are,
in general, greater than those computed in the framework of the ISGW2 model and
more favorable with the available experimental data. Specifically, our results
for exclusive channels $B \to \eta K_{2}^{*}(1430)$ and $B \to \phi
K_{2}^{*}(1430)$ are in agreement with recent experimental information.
