When you run a model in DS you automaticcaly get a dataitem with a log file with all the log4net messages that occured during model run.
'During' means the model is in a running state: (initializing,executing,finishing).
This is done RunningActivityLogAppender listening to changes in activities of activityrunner. So when a model goes to initializing the RALA keeps messages for that model. When the model finishes the RALA adds (or updates) a dataitem in the model.