Site-to-Site communication has received a major overhaul in ConfigMgr 2012 with the introduction of SQL replication replacing most of the legacy file transfer in and out of inboxes.
Changes in any Primary Site database will be replicated globally to all Sites in the hierarchy, not just the immediate parent or child.
To help monitor and resolve replication issues between the Sites there is a Database Replication node in the Monitoring section of the console that will show the status of any links.
The Replication Link Analyzer is an additional tool that enables further analysis and remediation of SQL replication issues between Sites. Note that content (for packages, applications and OS deployments) is still replicated using the file system.