For all intents and purposes

I've always wondered - is this the correct version of this idiom? I've heard "all intents and purposes," "all extents and purposes," "all extensive purposes," and left to my own devices, I tend to say "all intensive purposes." Intents and purposes sounds the most like something vaguely grammatical to me, but I still haven't a clue what it's supposed to mean anyway, outside of idiomatic use. I would use it to mean "essentially" or "effectively" or something to that effect, but what's the actual construction here? "For all intents and purposes.... it is?" Something like that? I never thought about it, because it's not really a phrase you see written down a lot.