To rent an office you'll first have to find a station with an open slot. Each station has 24 public office slots so 24 different corporations can have hangars there.
When at a station with available office space, click the Rent office button in the bottom right corner of the screen. Note that offices in player owned Outposts may be restricted for rental based on standings.
When you rent the office the rental fee is taken out of your corporation's wallet, and a bill for the next period is issued. You have to pay those bills manually, and can do so from anywhere: Open your corporation wallet, press the Bills tab and then the Payable tab. You should then see a list of the outstanding bills your corporation has. Find the bill you are looking for, right click it and select Pay bill. This will take the rent amount out of your corporation's wallet, so you won't have to worry about the slot for another period. All office bills are paid in advance.
The office price changes daily (at downtime) based on the number of free offices in the station. If no offices are free, the price goes up by 5%; if one office is free, the price stays the same; if more than one office is free, the price drops according to this formula: (Free_Offices - 1) / 23 * -5 (results in % change). The maximum drop per day is -5%, which happens when all offices are free. The minimum office rent is 10,000.00 isk.
To unrent an office you open your corporation hangar. On the bottom of the window you have a Unrent office button. When you click that and press Accept on the confirm window, you will no longer have an office at that station. The slot you had is then made publicly available. You can also unrent an office by not paying the bill.
Directors of a corporation may also unrent an office by right clicking and selecting the option in the details page of the corporation window home tab.
If you lose an office where your corporation has items, such as by forgetting to pay the bill or by unrenting the office, the items will be impounded. The CEO or directors of your corporation will have to go to that station and press the Corp Hangar button in the bottom right corner to get the items back. This costs 50% of the rental amount and drops the impounded items into their personal hangar. You must have office rental rights in the station in order to be allowed to use this feature, if the station is owned by a hostile entity you may be unable to release impounded items.
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