[Centos] How to cp a file to every subdirectory

[mike at CamaroSS.net (Mike Kercher)]

I need to copy a file (or actually a symlink) to every subdirectory on a
path.

I know that cp -s will do the copy I want, but how can I get it to go into
every subdirectory?  I've tried different iterations of ls to get a listing
of directories only (recursively) without success.

TIA

Mike