Skullsplitter is the ancestral weapon of House Dyser. It is a massive battle axe, one of the largest known in Westeros. It is known for its distinctive primal look and black metal handle and blade.
It was the trademark of Lord Anthor Dyser, right up until he was executed by Holden Frey, who took possession of it afterwards. Holden often disrespected the weapon and gloated about his ownership of it. However, after Holden was removed from power, Hendrick Grayburn took possession of the axe and had it returned to Falkirk, where it presumably went to Edric Dyser, the current Lord of Falkirk and the last male of the house.