  The conformal anomaly is computed on even $d$--spheres for a $p$--form
propagating according to the Branson--Gover higher derivative, conformally
covariant operators. The system is set up on a $q$--deformed sphere and the
conformal anomaly is computed as a rational function of the derivative order,
$2k$, and of $q$. The anomaly is shown to be an extremum at the round sphere
($q=1$) only for $k<d/2$. At these integer values, therefore, the entanglement
entropy is minus the conformal anomaly, as usual.
  The unconstrained $p$--form conformal anomaly on the full sphere is shown to
be given by an integral over the Plancherel measure for a coexact form on
hyperbolic space in one dimension higher.A natural ghost sum is constructed and
leads to quantities which, for critical forms, i.e. when $2k=d-2p$, are,
remarkably, a simple combination of standard quantities, for usual second
order, $k=1$, propagation, when these are available. Our values coincide with a
recent hyperbolic computation of David and Mukherjee.Values are suggested for
the Casimir energy on the Einstein cylinder from the behaviour of the conformal
anomaly as $q\to0$ and compared with known results written as alternating sums
over scalar values.
