  The Assouad dimension of the limit set of a geometrically finite Kleinian
group with parabolics may exceed the Hausdorff and box dimensions. The Assouad
\emph{spectrum} is a continuously parametrised family of dimensions which
`interpolates' between the box and Assouad dimensions of a fractal set. It is
designed to reveal more subtle geometric information than the box and Assouad
dimensions considered in isolation. We conduct a detailed analysis of the
Assouad spectrum of limit sets of geometrically finite Kleinian groups and the
associated Patterson-Sullivan measure. Our analysis reveals several novel
features, such as interplay between horoballs of different rank not seen by the
box or Assouad dimensions.
