The Frozen halls, and beyond. Lich King fight Speculation.

[Loganius]

That's... not how it works. You're fighting Arthas. He's evil. He doesn't give a rat's arse about harming whoever. He already took control over Ner'zhul and look where that got us. Please take the MUST... GAIN... CONTROL... OVER... EVIL SIDE crap somewhere else, because Ner'zhul isn't the big villain around here anymore.

When did he take control over Ner'zhul? Last I checked it was the other way around.

[Magnett]

http://www.wowwiki.com/Ner%27zhul

As the Lich King, Ner'zhul would rule the Scourge alone until his merger with Arthas Menethil, who would later consume his spirit to become the dominate spirit of the Lich King.

http://www.wowwiki.com/Arthas_Menethil

In that moment, Ner'zhul and Arthas' spirits fused into a single mighty being, just as the Lich King had always planned. Arthas as a single being ceased to exist, now one half of one of the most powerful entities Azeroth had ever known, the new Lich King.

While he dreamed, he banished his humanity and consumed his other half, creating the dominant entity of the Lich King.

It's in the Arthas: Rise of the Lich King novel. The Wowwiki article for the novel itself doesn't mention it, though.

Regardless, the Tirion's Gambit chain in Icecrown states that there is no possible redemption for Arthas. There will be no I SHALL SACRIFICE MYSELF TO RID THE LANDS OF THIS DEMON. There will just be the Lich King dying (..or running away) and I'm thankful for that.