I've been studying up on them. TONS of overhead. TONS.
First off, the whole concept of owning space is bugged. Think, UO housing in the early days. People report things being stolen, destroyed, invulnerable, broken and more. No idea how many play own things there are out there, so don't know percentages of problems. Many people report no problems at all as well.
All of what is below is how I'm interpreting things. I could be wrong, this is how I understand it.
First, there are towers or POS. They are used for mining, resource proccessing and stuff like that. Many people say they make millions per week with them, others say it's hard to break even. Don't know the building cost, but, these guys are the beginning to placing a station. The tower is vulnerable from attack, as well as neglect. I don't know what it takes, but one guy suggested a dread and a bunch of smaller fleet ships to cover the dread. But, you could bust through it's shields and destroy it. You could also forget to fuel it, which causes systems to shut down, including shields. You can also arm it with guns, launchers, etc. These guns can be programmed to shot people based on sec rating, or war status. So, if at war, or being attacked, park by a tower for added protection. You can store things there, but you can not dock in one. No station (or maybe limited station) capabilities. You need the password to access it. Putting one of these in an empty systems give you soverignty over that system. Once you have soverignty, you get to place a station. There are small, medium and large towers.
Once you have soverignty, you can place a station. Station is just like a regular station you've been using. You can only place them in .3 or less areas. Maybe not 0.0 as well, not sure one that. I'm guessing 0.0 is ok though, because there can be ONLY ONE player owned station in a system. So, land is limited. . . . Satations are invulnerable, sort of. They can never be destroyed. Once placed, they are always and forever there. However, they can change hands.
Capturing a station. To capture a station, you must gain soverignty over that system. You do this by placing the towers mentioned above. Once you have more towers than the current owners, you can now attack the station and take down it's shields. Once the shields are gone, you have yourself a station. You must maintain soverignty of the system to maintain control of the station. So, if enemy/target corp has 5 towers, you can place 6, and gain control. Or, you could destroy all his towers, and build one of your own, and gain control.
Along with the above, there are timers and what not that have to expire. As in, once you gain soverignty, I think it's like 5 days before you can take down the shields and actually capture the stations. That way, stations can't change hands over night and stuff. Current owners of a station get mail messages saying their towers are being attacked, or, another corp has built a tower. So, capturing is possible, however, it is a major undertaking.
So, that's it for now.