  This article studies point-vortex models for the Euler and surface
quasi-geostrophic equations. In the case of an inviscid fluid with planar
motion, the point-vortex model gives account of dynamics where the vorticity
profile is sharply concentrated around some points and approximated by Dirac
masses. This article contains three main results with several links between
each other. In the first part, we provide two uniform bounds on the
trajectories for Euler and quasi-geostrophic vortices related to the
non-neutral cluster hypothesis. In a second part we focus on the Euler
point-vortex model and under the non-neutral cluster hypothesis we prove a
convergence result. The third part is devoted to the generalization of a
classical result by Marchioro and Pulvirenti concerning the improbability of
collapses and the extension of this result to the quasi-geostrophic case.
