Ultra-dense networks (UDNs) envision the massive deployment of heterogenous base stations (BSs) to meet the desired traffic demands. Furthermore, UDNs are expected to support the diverse devices e.g., personal mobile devices and unmanned ariel vehicles. User mobility and the resulting excessive changes in user to BS associations in such highly dense networks may however nullify the capacity gains foreseen through BS densification. Thus there exists a need to quantify the effect of user mobility in UDNs. In this article, we consider a three-dimensional N-tier downlink network and determine the association probabilities and inter/intra tier handover rates using tools from stochastic geometry. In particular, we incorporate user and BSs' antenna heights into the mathematical analysis and study the impact of user height on the association and handover rate. The numerical trends show that the intra-tier handovers are dominant for the tiers with shortest relative elevation w.r.t. the user and this dominance is more prominent when there exists a high discrepancy among the tiers' heights. However, biasing can be employed to balance the handover load among the network tiers.