Due to the time-varying channels with line-of-sight (LoS) and non-LoS (NLOS) components, the handover (HO) trigger locations of unmanned aerial vehicle (UAV)-assisted networks are irregular and fluctuating, which causes frequent HOs and HO failures (HOFs). However, existing works only consider path loss and cannot obtain sound HO parameters. In this paper, the HO events trigger locations are explicitly modeled as time-varying boundaries, where the UAV altitude and LoS/NLoS components are projected to geometric boundaries satisfying the conditions of HO events, and the fluctuation of boundaries is introduced by modeling their radii as random variables with fast fading coefficients. Based on specific received signal ratios of HO events, the distributions of HO event boundaries are derived via the projection criterion. Specifically, the HO trigger location is analyzed through the HO boundary considering the measurement period, then HO status during Time-to-Trigger is analyzed via HO event boundaries and user-UAV geometric relationship. Expressions of HO events in UAV-assisted networks, including HO, HOF, and ping-pong (PP), are obtained with and without fast fading. The results show more HOs, HOFs, and PPs occur with fast fading, which increase by 1.7x , 1.4x, and 3.1x when densities of the MBS and UAV are 10/km(2 )and 100/ km(2).