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To hire a TL, you need to find any of the Supply TLs flying around the universe then comm the captain. If the ship is available, the option to hire will be available, if not, then the TL is currently busy so you need to either wait or find another one.
The TL will charge a small fee for every gate they travel through, so hiring one a long way away will not only take a lot of time but also cost more money.
Most idle TL's will be found in faction core sectors where there are shipyards, most shipyard sectors will have 2 TLs available.
Once hired, you will need to comm the TL's Captain to give it orders.
The hired ship will be displayed in your Property Owned menu, and you will be able to see where it is on the sector map. You can comm the ship directly from here.
1.2 Buying Station Kit
Once you have a TL (either hired or owned) you need to send it to the place to buy or pickup the station kit. Station kits can be bought at most faction shipyards, or produced at your own Headquarters once you have unlocked the blueprint.
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Once its docked, access the trade menu of the shipyard, and the station kits should now be available to buy (assuming you have the required notoriety).
Notice some of the stations are in Red, where as some just have the "ST" in Red.
The Red station name indicates you do not have enough notoriety with the station owner to buy it.
This will be displayed at the bottom of the Trade menu for the currently selected item
The Left side is your Current Notoriety and the Right side is what you need, so to buy the Computer Plant, you will need to increase your rank 1 more level.
If just the "ST" value is red, which is your Transport Class, this indicates that it will not fit in your current ship because its too small. For station, it means you dont currently have an available TL docked (either yours or hired).
NOTE: if you are in space, you will require your ship to be equipped with the Trading Systems Extension, otherwise you will need to be docked at the shipyard as well as the TL.
1.2.2 Building at your Headquarters
Instead of buying a station kit from a shipyard, you can also build them from resources at your Headquarters.
First of all, you need to use Diplomacy to obtain the blueprint so its available to build.
To start building the station, you need to open the Station Parameters menu
In the "Adjust Production Queue" section, you will find the option to select a blueprint.
This displays the Blueprints menu, where you can select the blueprint you wish to add to the queue.
The tabs at the top allow you to filter the list by type and race to make it easier to find what you are looking for if you have alot of blueprints.
NOTE: you can also use the search bar (SHIFT+F) to search for a specific item.
On the right of your screen you will also see the list of resources required to built the item
This includes how long it'll take to build (Cycle time). Any wares in red indicate you do not currently have enough resources in your Headquarters.
Once added to the queue, you can change the quantity to build, setting this to 0 will remove it from the queue. Once there are enough resources available, and the production queue is empty, it'll start to produce it. Once it starts production, you can not cancel it.
With the item in the queue select, it will also display the resource menu to the right, so you can see what else you might be missing if it doesn't start
NOTE: there is a delay before it starts producing, so if you have all the resources and its not started production, you may just need to wait a short time.
Once its producing, you can see it displayed along with the program and remaining time.
You can also view the production in the station info menu.
the "Reserved" section is for when a station is being built, the Headquarters will reserve enough space to put the station kit once its built. This prevents you from filling the Headquarters and then not having enough room once the station is produced.
Once its produced, it will appear in the Stations section in your headquarters. Here you can transfer it to a docked TL.
To transfer it, first select the TL you want to transfer it to (IE via your Property Owned Menu) then select "Adjust Station Parameters" like above. When you do this via your TL, then the TL becomes the target ship for transferring wares too. This can also be done on a Hired TL as well.
1.3 Building the Station
Once you have the station kit on a TL you can then build it. You need to move the TL to the sector you wish to build in, and you must also be present in the same sector.
You both you and your TL are in the Target sector, you can then build the station
1.3.1 Building via Hired TL
1.3.2 Building via Owned TL