Several protocol efficiency metrics (e.g., scalability, search success rate, routing reachability and stability) depend on the capability of preserving structure even over the churn caused by the ad-hoc nodes joining or leaving the network. Preserving the structure becomes more prohibitive due to the distributed and potentially uncooperative nature of such networks, as in the peer-to-peer (P2P) networks. Thus, most practical solutions involve unstructured approaches while attempting to maintain the structure at various levels of protocol stack. The primary focus of this paper is to investigate construction and maintenance of scale-free topologies in a distributed manner without requiring global topology information at the time when nodes join or leave. We consider the uncooperative behavior of peers by limiting the number of neighbors to a pre-defined hard cutoff value (i.e., no peer is a major hub), and the ad-hoc behavior of peers by rewiring the neighbors of nodes leaving the network. We also investigate the effect of these hard cutoffs and rewiring of ad-hoc nodes on the P2P search efficiency.