Despite promising capacity gains, small cell densifications in ultra-dense HetNets can lead to frequent handovers (HOs), which may cause significant network overheads and decline in user experience. With the aim of modelling handovers in the context of ultra-dense HetNets, we propose a novel approach to model coverages of overlapping small cells. Based on this model, we derive the cumulative distribution function (CDF) of the user equipment's (UE) time-of-stay in small cells using boundary length and chord length distributions of small cell coverage. Our model is comprehensive enough to capture the nature of both inter-tier and intra-tier HOs in small cell networks, the latter of which is a major challenge in ultra-dense HetNets. Our analytical results can provide guidance for optimisations of HO parameters based on user velocity and small cell density to reduce network overheads and improve user experience.