I don't understand how can it be at the same time defined, == 0, and eq "".

This is easy. The return value is the empty string !1^† as bart says.

$ perl -le 'print "yes" if defined ""'
yes
$ perl -le 'print "yes" if 0 == ""'
yes
$ perl -le 'print "yes" if "" eq ""'
yes
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The bigger question you are asking—basically, why the empty string is returned—doesn't seem to have such a clear answer. This has come up recently in the discussion that followed Re^4: Unhappy returns. You'll find a closer look at the more general issue including how other statements are handled there. FWIW, I think it should probably be considered a bug. I'm pretty sure it isn't documented.

Which is exactly the same as the empty string only, uh, different It doesn't cause warnings where an empty string would.

Edit: Corrected "empty string" to !1 per bart's response below and added footnote.

-sauoq
"My two cents aren't worth a dime.";