Ground Layer Adaptive Optics: PSF effects on ELT scales

On certain extent the behavior of the Adaptive Optics correction for Extremely Large Telescope scales with diameter size. But in Ground Layer Adaptive Optics the combined effect of a Large Field of View and the large overlap of Guide Stars pupil footprints at high atmospheric altitude introduces severe changes in the behavior of the correction returning a very different distribution of the energy going from known 8-10meter to 100m diameters. In this paper we identify the reasons and the ways of these different behaviors.