Current ruling house. House Arabasti won the competition against House Prophyria to claim leadership of Korvosa.
House Arbasti came from Cheliax during their Apostate Rebellion. Himself related to the current Queen of Cheliax via marriage. Eodred I was the first King of Korvosa. However the city’s charter recognizes Cheliax as it’s ruler and that Korvosa tends Varisia on their behalf. To date, the Thrice Damned House of Thrune has never acknowledged a monarch of Korvosa as anything more than a mayor of some backwater colony in the wilderness.
Following Eodred I was Cardraith I who was terrible and vicious and died of a mysterious fit. Korvosa was, for a time, ruled by a Prophyrian monarch until cut short by the arrival of a heir to the Arabasti line: Domina Arabasati from Cheliax.
Queen Domina got. shit. done. ok? She improved relations with Cheliax several hundreds fold leading to the money raised being put to use for public works and buildings such as the Great Tower, Citadel Vraid, and Domina’s Wall. Korvosans look back on her reign as its golden age.
Eodred II, the current king of Korvosa, follows Domina’s footsteps with more public works, however with coffers dwindling, many of these have suspended progress. He also is a known womanizer with a harem of girls and women from all across the world.