  The recently introduced second order total generalised variation functional
$\mathrm{TGV}_{\beta,\alpha}^{2}$ has been a successful regulariser for image
processing purposes. Its definition involves two positive parameters $\alpha$
and $\beta$ whose values determine the amount and the quality of the
regularisation. In this paper we report on the behaviour of
$\mathrm{TGV}_{\beta,\alpha}^{2}$ in the cases where the parameters $\alpha,
\beta$ as well as their ratio $\beta/\alpha$ becomes very large or very small.
Among others, we prove that for sufficiently symmetric two dimensional data and
large ratio $\beta/\alpha$, $\mathrm{TGV}_{\beta,\alpha}^{2}$ regularisation
coincides with total variation ($\mathrm{TV}$) regularisation.
