Anisotropies are an important tool to distinguish between different origin and primary models for the UHECRs, nicely complementing the information on the energy spectrum and chemical composition. We have briefly summarized several signatures which one expects to show up in the pattern of ultra-high energy cosmic ray (UHECR) arrival directions at different energies. In particular, we have commented upon the broad maximum of the two-point autocorrelation function within a scale of 20 degrees - 30 degrees found in this document in the combined UHECR data arrival directions, and recently confirmed by Auger. At the moment, the most likely explanation seems to be that the signature reflects the large scale structures (LSS) distribution of UHECR sources, probably of nearby ones. The autocorrelation analyses reported in this paper show that this interpretation is indeed favored in particular if the effective horizon is smaller than the GZK one for protons of the assumed energy.