We study network formation in which nodes enter sequentially and form connections through a combination of random meetings and network-based search, as in Jackson and Rogers (2007). We focus on the impact of agents' heterogeneity on link patterns when connections are formed under type-dependent biases. In particular, we are concerned with how the local neighborhood of a node evolves as the node ages. We provide a surprising general result on "long-run integration" whereby the composition of types in a node's neighborhood approaches the global type distribution, provided that the search part of the meeting process is unbiased. Integration, however, occurs only for sufficiently old nodes, while the aggregate distribution of connections still reflects the bias of the random process. For a special case of the model, we analyze the form of these biases with regard to type-based degree distributions and group-level homophily patterns. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals.