  We investigate the stellar and dynamical mass profiles in the centres of 25
brightest cluster galaxies (BCGs) at redshifts of 0.05 $\leq z \leq$ 0.30. Our
spectroscopy enables us to robustly measure the Gauss-Hermite higher order
velocity moments $h_{3}$ and $h_{4}$, which we compare to measurements for
massive early-type galaxies, and central group galaxies. We measure positive
central values for $h_{4}$ for all the BCGs. We derive the stellar
mass-to-light ratio ($\Upsilon_{\star \rm DYN}$), and velocity anisotropy
($\beta$) based on a Multi-Gaussian Expansion (MGE) and axisymmetric Jeans
Anisotropic Methods (JAM, cylindrically- and spherically-aligned). We
explicitly include a dark matter halo mass component, which is constrained by
weak gravitational lensing measurements for these clusters. We find a strong
correlation between anisotropy and velocity dispersion profile slope, with
rising velocity dispersion profiles corresponding to tangential anisotropy and
decreasing velocity dispersion profiles corresponding to radial anisotropy. The
rising velocity dispersion profiles can also indicate a significant
contribution from the intracluster light (ICL) to the total light (in
projection) in the centre of the galaxy. For a small number of BCGs with rising
velocity dispersion profiles, a variable stellar mass-to-light ratio can also
account for the profile shape, instead of tangential anisotropy or a
significant ICL contribution. We note that, for some BCGs, a variable
$\beta_{z}(r)$ (from radial to tangential anisotropy) can improve the model fit
to the observed kinematic profiles. The observed diversity in these properties
illustrates that BCGs are not the homogeneous class of objects they are often
assumed to be.
