  In dynamo power-based scaling laws, the power $P$ injected by buoyancy forces
is measured by a so-called flux-based Rayleigh number, denoted as ${\rm
Ra}_Q^*$ (see Christensen and Aubert, 2006). Whereas it is widely accepted that
this parameter is measured (as opposite to controlled) in dynamos driven by
differential heating, the literature is much less clear concerning its nature
in the case of imposed heat flux. We clarify this issue by highlighting that in
that case, the ${\rm Ra}_{Q}^*$ parameter becomes controlled only in the limit
of large Nusselt numbers (${\rm Nu} \gg 1$).
  We then address the issue of the robustness of the original relation between
$P$ and ${\rm Ra}_Q^*$ with the geometry and the thermal boundary conditions.
We show that in the cartesian geometry, as in the spherical geometry with a
central mass distribution, this relation is purely linear, in both differential
and fixed-flux heating. However, we show that in the geometry commonly studied
by geophysicists (spherical with uniform mass distribution), its validity
places an upper-bound on the strength of the driving which can be envisaged in
a fixed Ekman number simulation. An increase of the Rayleigh number indeed
yields deviations (in terms of absolute correction) from the linear relation
between $P$ and ${\rm Ra}_Q^*$. We conclude that in such configurations, the
parameter range for which $P$ is controlled is limited.
