In comments, Penny mentions her attitude about owning systems in wspace:
As I got in to a discussion before, it's not that we think we own the system, but more that trying to share a system with neutrals in a class of space where NBSI is pretty standard is awkward, to say the least.(We discussed this some at tigerears back before I moved into my current system. Here is the post.) It is certainly true that sharing with strict NBSI is hard. But just setting each other blue is not difficult. But that's not what interested me here: it was the reminder of our earlier disagreement.
Me, I think I own my system. I own it in the one sense that matters: force. I have a big advantage in force projection in my system, because I already have ships there. Further, I am probably willing to spend more to safeguard my system than anyone else is to take it. I have a multi billion ISK investment, and nobody else does. Part of the way I achieve superior force is about obscurity: there are plenty of people that could take my system, but they'd have to find it first, and that's not easy. And even if they did, they would not gain anything because they don't want to live deep in wspace. Part of it is the difficulty in getting in forces: a C4 system will allow in only about 20 battleships (100m kg each) or 120 battlecruisers (14m kg per).
Another aspect of ownership in lower wspace is capitals. In C1 through C4, no wormhole can pass even a single capital ship. The only way to get a capital ship in these systems is to build it there. If you live in a system and have built a capital or two, you have a massive advantage over anyone attempting to displace you. With a dreadnaught you can reinforce their tower in an hour using one pilot. They can reinforce yours only after hours of boring structure-shooting with 20 pilots. With a carrier you repair your tower and/or POS parts in an hour. The enemy would have to sit out in repping cruisers for hours. Force economy means more effective force.
Penny is right, though, inasmuch as she construes "owning" to mean something more than occupation. There is no registry of wormhole ownership. (It is interesting to think about trying to implement one.) If you leave a wspace system, de facto you no longer own it.
Personally, I find the way nullsec "sovereignty" works completely upside down and wrong. In EVE, "sovereignty" is an actual attribute that is held in their database, known universally for every system. To get it, you have to put up special structures. Once these are online, you get "sovereignty", and its benefits, even if you never lift a finger to fight in that system. Note that I am scare-quoting "sovereignty" here exactly to highlight the artificial nature of what you are getting. Real sovereignty is the power of ultimate decision. Real sovereignty is a function of power, which flows from the barrel of a gun. In EVE sovereignty is a system attribute that allows you certain privileges, particularly lower fuel costs and to be allowed to anchor certain improvements.
In the real world, sovereignty is superior force. It is not mediated by any structures. When the US Army occupies a country, it does not immediately put up special statues to claim the area, nor are there special statues that it has to tear down. Well, unless you want to analogize armies themselves to special statues, in which case the analogy kind of goes through. But of course we already have armies in EVE -- fleets.
Wspace shows the way sovereignty ought to work. You are sovereign if you have superior force.