We consider systems for data sharing among heterogeneous peers related by a network of schema mappings. Each peer has a locally controlled and edited database instance, but wants to ask queries over related data from other peers as well. To achieve this, every peer’s updates propagate along the mappings to the other peers. However, this update exchange is filtered by trust conditions — expressing what data and sources a peer judges to be authoritative — which may cause a peer to reject another’s updates. In order to support such filtering, updates carry provenance information. These systems target scientific data sharing applications, and their general principles and architecture have been described in [21]. In this paper we present methods for realizing such systems. Specifically, we extend techniques from data integration, data exchange, and incremental view maintenance to propagate updates along mappings; we integrate a novel model for tracking data provenance, such that curators may filter updates based on trust conditions over this provenance; we discuss strategies for implementing our techniques in conjunction with an RDBMS; and we experimentally demonstrate the viability of our techniques in the Orchestra prototype system. This technical report supersedes the version which appeared in VLDB 2007 [17] and corrects certain technical claims regarding the semantics of our system (see errata in Sections [3.1] and [4.1.1]).