  Given a regular bounded domain $\Omega\subset\R{2m}$, we describe the
limiting behavior of sequences of solutions to the mean field equation of order
$2m$, $m\geq 1$, $$(-\Delta)^m u=\rho \frac{e^{2mu}}{\int_\Omega
e^{2mu}dx}\quad\text{in}\Omega,$$ under the Dirichlet boundary condition and
the bound $0<\rho\leq C$. We emphasize the connection with the problem of
prescribing the $Q$-curvature.
