I thought it was pretty straight-forward. Ner’zul > Arthas + Ner’zul > Essentially just Arthas*

• Arthas and Ner’zul’s consciousness merge when Arthas puts on the Helm of Domination. What follows is a battle inside the Lich King where Arthas and Ner’zul’s consciousnesses duke it out for full control. Arthas wins out because Ner’zul didn’t expect his will to be so strong and so Arthas essentially becomes the Lich King. After which he detects a faint glow of humanity inside him and sees it as detrimental. He rips out his heart and casts it out hoping it would be enough. As fallen prince and leader of the Scourge, Arthas decides to consolidate his power and build up his forces + defenses for an assault on the world.