[Hampshire] Replicating directory tree and filenames

I want to replicate a huge (multiple TBs) directory tree such that the
replica has the same files, same GIDs/UIDs as the original, same paths, but
with all the files 0 bytes. In other words, copy the directory and file
structure but not the data. It feels as if this should be easy to do, but
I haven't thought of an easy way yet...

Keith