If I propose and start and new overflow/exchange site, would I become the owner of it? Or is there any ability for me to own it if I play a big role in making it successful?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Basically, no. Content contributed to SE sites is owned by the poster (I think? don't quote me on that); the underlying technology as well as the look of the site etc. are owned by Stack Exchange Inc.
In the days of Stack Exchange 1.0, they tried a model in which you would own (or at least maintain primary control over) the sites you created, but it generally didn't work out well because without the support of the SE team, most of the sites fizzled out.
You do not own it. Stack Exchange owns it.
You would be in a great position to be a moderator for that site, but that's about it.