In fully three-dimensional (3D) positron emission tomography (PET) imaging, the scatter fraction (SF) is about 40%-60%, which may degrade the imaging quality severely. Scatter correction is important for high quality image reconstruction. Model-based scatter correction has been proved to be accurate and available in clinical PET. However, it does not correct the scatter from out of the field of view (OFOV) and multiple scatters. In this study, we demonstrate the radial and axial distribution of scatters from OFOV when the source is located in different radial positions. In order to apply the above conclusions to different PET systems, we characterize the scatters from OFOV as a function of the ratio of the scanner diameter to the length of the axial field of view (AFOV) by modeling several typical whole-body and micro PET systems. The proportions of true events (S0 0), single scatter of one photon (S1 0), single scatter of both photons (S1 1), double scatter of one photon (S2 0) and multiple scatter (Sm) are also calculated and compared. Here the 3D-PET Monte Carlo simulations are performed with the Geant4 Application for Tomography Emission (GATE). In summary, the scatters from OFOV tend to be recorded on the lines of response (LOR) far away from the source. They have a much more serious impact on whole-body PET than micro PET depending on the ratio of scanner diameter to the length of AFOV. In whole-body PET, twice scatters including single scatter of both photons (S1 1) and double scatter of one photon (S2 0) add up to about 12% so that twice scatter correction must be taken into account to acquire a high quality reconstruction image. In fully three-dimensional (3D) positron emission tomography (PET) imaging, the scatter fraction (SF) is about 40% -60%, which may degrade the imaging quality severely. Scatter correction is important for high quality image reconstruction. Model- based scatter correction has been proved to be accurate and available in clinical PET. However, it does not correct the scatter from out of the field of view (OFOV) and multiple scatters. In this study, we demonstrate the radial and axial distribution of scatters from OFOV when the source is located in different radial positions. In order to apply the above conclusions to different PET systems, we characterize the scatters from OFOV as a function of the ratio of the scanner diameter to the length of the axial field of view ( AFOV) by modeling several typical whole-body and micro PET systems. The proportions of true events (S0 0), single scatter of one photon (S1 0), single scatter of both photons (S1 1), double scatter of one photon S2 0) and mu Here, the 3D-PET Monte Carlo simulations are performed with the Geant4 Application for Tomography Emission (GATE). In summary, the scatters from OFOV tend to be recorded on the lines of response (LOR They have a much more serious impact on whole-body PET than micro PET depending on the ratio of scanner diameter to the length of AFOV. In whole-body PET, twice scatters including single scatter of both photons ( S1 1) and double scatter of one photon (S2 0) add up to about 12% so that twice scatter correction must be taken into account to acquire a high quality reconstructed image.