  We study the radiative $B \to K \eta^{(\prime)} \gamma$ decays, which are
important to investigate CP violation, and are also relevant to assess the role
of the exclusive modes induced by the $b \to s \gamma$ transition to saturate
the inclusive $B \to X_s \gamma$ decay rate. Moreover, these channels do not
display the same hierarchy as $B \to K \eta^{(\prime)}$ modes, for which the
decay into $\eta^\prime$ is enhanced with respect to one into $\eta$. The
three-body radiative decays reverse the role: we find that this experimentally
observed behavior (although affected by a large uncertainty in the case of the
$\eta^\prime$) is reproduced in the theoretical analysis. We compute a $B^* \to
K$ form factor, needed for this study, using light cone QCD sum rules, and
discuss a relation expected to hold in the large energy limit for the light
meson. Finally, we examine $B\to K \eta \gamma$ in two extensions of the
standard model with universal extra dimensions, to investigate the sensitivity
of this rare mode to such a kind of new physics effects.
