To search and delete empty files in the current directory and subdirectories:
find . -type f -empty -delete
-type f
is necessary because also directories are marked to be of size zero.
The dot .
(current directory) is the starting search directory. If you have GNU find (e.g. not Mac OS), you can omit it in this case:
find -type f -empty -delete
From GNU find
documentation:
If no files to search are specified, the current directory (.) is used.