It's not logging related to replication.
When you have transactional replication, the space in the database's transaction log cannot be marked reusable until the log records have been replicated. Hence if the replication is broken the space in the log can't be reused. Hence the log will grow until it fills the disk.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability