The scalability of BGP routing is a major concern for the Internet community. Scalability is an issue in two different aspects: increasing routing table size, and increasing rate of BGP updates. In this paper, we focus on the latter. Our objective is to characterize the churn increase experienced by ASes in different levels of the Internet hierarchy as the network grows. We look at several ``what-if'' growth scenarios that are either plausible directions in the evolution of the Internet or educational corner cases, and investigate their scalability implications and interaction with different failure types. Our findings explain the dramatically different impact of multihoming and peering on BGP scalability, highlight negative and positive effects of multihoming on churn and reachability, and identify which topological growth scenarios will lead to faster churn increase for different failure types.