What is limiting near-infrared astrometry in the Galactic Centre?

We systematically investigate the error sources for high-precision astrometry from adaptive optics (AO) based near-infrared imaging data. We focus on the application in the crowded stellar field in the Galactic Centre. We show that at the level of less than or similar to 100 mu as a number of effects are limiting the accuracy. Most important are the imperfectly subtracted seeing haloes of neighbouring stars, residual image distortions and unrecognized confusion of the target source with fainter sources in the background. Further contributors to the error budget are the uncertainty in estimating the point-spread function, the signal-to-noise ratio induced statistical uncertainty, coordinate transformation errors, the chromaticity of refraction in Earth's atmosphere, the post-AO differential tilt jitter and anisoplanatism. For stars as bright as m(K) = 14, residual image distortions limit the astrometry, for fainter stars the limitation is set by the seeing haloes of the surrounding stars. In order to improve the astrometry substantially at the current generation of telescopes, an AO system with high performance and weak seeing haloes over a relatively small field (r less than or similar to 3 arcsec) is suited best. Furthermore, techniques to estimate or reconstruct the seeing halo could be promising.