Vortex precession was simulated in two-dimensional magnetic dots. The Landau-Lifshitz equation with exchange and dipolar interactions was integrated at a low temperature with initial conditions consisting in a single vortex situated aside from the central position. This vortex precesses around the center of the sample and either can be expelled or converges towards the center. These relaxation processes are systematically studied. A simple qualitative explanation of the observed behaviors is proposed, including seemingly somewhat erratic ones. Intrinsic pinning of the vortex motion, unconnected with defects, is also observed and an explanation thereof provided. (C) 2011 Elsevier B.V. All rights reserved.