What is structure/hiearchy of IP addresses?

I mean, is mandatory that IP address e.g. is subnet of Of course many times that is the case and IMO it would be logical, but I have heard that you can own IP address space. I think only way that can work is there is now structure like this and can be under e.g.

That bring another questions, how routing works? Of course regardless those exections usually routers can route hiearchy piece by piece starting from first number of the IP addr to last one, but not always. Is that the case? Normally routing is hiearchy process, but few of hops are with execptions. Autonomous systems need tell with BGB that there is hiearchy address space, but remember one execption inside that space. For example, space and somepoint inside is IP

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