I use SugarSync to automatically synchronize my data files between multiple computers.

Other possibilities include IDrive, Syncplicity, Windows Live Mesh (Beta), and Dropbox (Beta).

This is possible if JJ is the only person accessing the files. If not, as you say, a file could be changed at same time and it is not easy to sync to changes to the file.

Here is how I do it.

- Install MS SyncToy on work PC (free download from MS, requires .Net)

- At work, create a Sync pair between the work hard drive and the external hard drive.

- Run SyncToy before leaving work. Only changed files are copied to the external hard drive.

- At home, if possible work from the external hard drive.

- If it is not possible to work from the external hard drive, install SyncToy on the home PC and create sync pair. Run SyncToy sync before starting and after finishing work.

- When returning to work, run SyncToy sync before being work.

- Repeat as necessary

This is a little bit tedious but does work as long as only JJ accesses the files. Working from the external hard drive when at home simplifies the process a lot (only need to run SyncToy sync at work).

SyncToy is the only free sync tools that I have found that syncs deletions.