Quickly. Morgoth was already defeated and there was no reason for a duel. Some accounts give that Ëonwë was a superior fighter to Morgoth, regardless.

I don't really want to answer the question, since I'm more curious as to why you even need to know? I mean if I said he was squished into a little ball and Uinen kicked him into the void would you have any evidence to dispute it?

Still confused.

Myths Transformed:

"The war was successful, and ruin was limited to the small (if beautiful) region of Beleriand. Morgoth was thus actually made captive in physical form and in that form taken as a mere criminal to Aman and delivered to Námo Mandos as judge - and executioner. He was judged, and eventually taken out of the Blessed Realm and executed: that is killed like one of the Incarnates. It was then made plain (though it must have been understood beforehand by Manwë and Námo) that, though he had 'disseminated' his power (his evil and possessive and rebellious will) far and wide into the matter of Arda, he had lost direct control of this, and all that 'he', as a surviving remnant of integral being, retained as 'himself and under control was the terribly shrunken and reduced spirit that inhabited his selfimposed (but now beloved) body. When that body was destroyed he was weak and utterly 'houseless', and for that time at a loss and 'unanchored' as it were. We read that he was then thrust out into the Void. That should mean that he was put outside Time and Space, outside Eä altogether; but if that were so this would imply a direct intervention of Eru (with or without supplication of the Valar)."

^ What is Myths Transformed (fixed spelling)? And why should we trust it?

It's from the tenth volume of The History of Middle-earth.

So Morgoth's Ring. Okay. From that Morgoth was greatly weakened before he was cast into the void and as I suspected, none of the Ainur actually did it.

Takes a Valar god to cast out a Valar god