-- the system transfers only an abstract notion of ownership. It doesn't have the ability to transfer full ownership, by which I mean all of the capabilities, rights, and responsibilities commonly inferred by that term.
Exactly, you got it. The new owner will never know the private key of the previous owner, but the previous owner proved by signing the massege + transferring Bitcoin to the new owner that they are willing to transfer the 'ownership' to the new owner.
It is something new, but it works
