Remove Spaces from Filenames

How can I eliminate spaces in all my filenames?

This 'sh' shell script will do the trick, providing no two filenames in a directory differ by only spaces, and no directory names have spaces.

% cat sh2
#!/bin/sh
target_fn=$( echo $1 | tr -d " " )
if [ ! "$1" = "$target_fn" ]; then
  echo mv "$1"  "$target_fn"
  mv "$1"  "$target_fn"
fi


% ls -R1
.:
dirname
file name
file2 name
sh
sh2
tsh


dirname:
file2 name
file3name


% find . -print0 | xargs -0 -n1 ./sh2
mv ./dirname/file2 name ./dirname/file2name
mv ./file name ./filename
mv ./file2 name ./file2name


% ls -R1
.:
dirname
file2name
filename
sh
sh2
tsh


dirname:
file2name
file3name