  We give an explicit realization of the $\eta$-convolution power of an
$A$-valued distribution, as defined earlier by Anshelevich, Belinschi, Fevrier
and Nica. If $\eta:A\to A$ is completely positive and
$\eta\geq\operatorname{id}$, we give a short proof of positivity of the
$\eta$-convolution power of a positive distribution. Conversely, if
$\eta\not\geq\operatorname{id}$, and $s$ is large enough, we construct an
$s$-tuple whose $A$-valued distribution is positive, but has non-positive
$\eta$-convolution power.
