Islands that are occupied by other players or computer players can be taken over by other players in two different ways.
A player has to first declare war on the owner of the island (or have ships with items equipped and active that allow ships to attack without declaring war, such as the Letter of Marque). Then the player needs to use military ships to attack the main harbor and coastal buildings of the island. After the morale of the island reaches a critical point the player is prompted with two options: Either gain all the shares for that island, or conquer the island. If the player chooses to conquer the island the player will take over the island and claim it, with everything previously built on the island being removed. However, the harbor will keep its upgraded status. If a player chooses instead to claim all the shares of the island, the island will remain controlled by the current owner and instead the player will receive all share revenue from that island, with the later possibility to purchase the island outright using an economic takeover.
If a player buys all the shares of an island (displayed as a pie chart next to the island name), he/she will have the possibility to conquer the island by buying it. After claiming all 5 shares the player can select the middle of the share diagram. This is very costly as it requires 10 influence per share (in comparison to a big island which usually costs 30-40 influence to settle) and there is a 10 minutes timeout between the buying actions.
Small outposts owned by NPC traders and pirate fortresses cannot be taken over in any way, although pirate fortresses can be pacified using force, or by signing ceasefire or trade rights agreements with the pirate NPC.
If 2 or more players are attacking the same island together there will be no option to conquer the island. The only option is to accept shares for the island distributed based on how much each player contributed to the attack.
The 4 plateaus in The Arctic can only be taken over via shares.