Bear in mind accounts are separate from profiles - so to hand over an account, you would need to give the new user your email address as well.
Org profiles can be owned by multiple users - if there is only one user, then yes, they become the owner, although they could add other owners if they wished. 

So, the last member that remains in the organization, is the owner of the profile? 

Now owner of the account is always creator, but all org's admins can switch to the org and actually have full access to it, full org handover to another account isn't implemented yet.