The main RuneScape Wiki has an article on: Skull (PKing)
The Old School RuneScape Wiki also has an article on Skull (PKing).

A player with a PKing Skull

The Player Killing Skull shows above player who has attacked another player in the Wilderness in the past 20 minutes. Upon death with a skull, the player will lose ALL of their carried items, as opposed to saving the three most valuable, though having the Protect Items prayer activated allows one item to be saved on death.

You do not receive a skull for participating in Duels. This is because they are 'safe', as all items are retained upon death, and therefore not lost.

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