The sistem is run by a miriad of different servers that are own each by its community, you would have to research more deeply the specific server you want to know the owner of
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No one.
There are people who develop the software for different instances, but they don't implement it so they don't have control over what gets done with their software.
Different admins have control over their own servers, but they don't have control over other people's servers. This has already come up as one server defederated (dropped their connection with) other servers temporarily due to spam issues.
Mods control their own communities, but under the greater control of the admins for that server.
It is kind of like email or the world wide web. No one owns either of those.
I have a personal Lemmy instance, and a personal Calckey instance. Still debating on creating a personal PixelFed instance, and maybe even a public kbin instance.
Anyone who wants to host a fediverse website owns the fediverse. It belongs to any of us and all of us.