If I own a domain do I own all of its sub domains?

If I own a domain do I own all of its sub domains?

For example if I purchase example.com, do I automatically own mail.example.com, blog.example.com, etc?

If I do not own the sub domains, can anyone buy mail.example.com if I own example.com? Do I have a right of first sale if someone tries to buy one of my sub domains?

Finally, do the answers to the above questions apply to all domains in all TLDs, like .org, .net, .ca, .name, etc?

Thank you.

EDIT: According to the .name agreement registration restrictions at

http://www.icann.org/en/about/agreements/registries/name/appendix-11-25mar11-en.htm

an individual can register a .name domain only if the domain matches the eligibility requirements. There are several eligibility requirements, one of which is that a .name domain must be the real name or identifier of an individual. So, for example, firstname.lastname.name and firstnamelastname.name are both valid. However, lastname.name is not valid because it does not identify an individual. If I registered lastname.name, someone else could mount a challenge based on the eligibility requirements and register otherfirstname.lastname.name. So I do not in fact control the sub domains.

Am I reading that right? Are there similar restrictions on ownership of subdomains in other TLDs?

Yes, you own and control the entire namespace below the domain you purchase, because DNS is hierarchical. Creating mail.example.com and blog.example.com is just a matter of adding entries to the DNS zone that you control.

Since you asked about the name. domain, I'll address that specifically: You cited its eligibility requirements and have confused this with domain control. If you aren't eligible to have the domain to begin with, then the point is moot.

In the case of name. and a few other top level domains, it may be valid to register a second-level, third-level or a fourth-level name, depending on that domain's individual eligibility requirements. For instance, us. allows second-level registrations to anyone, but for historical reasons, there exist many second-level registrations corresponding to U.S. states which are registered to state government agencies, and where the third or fourth level is further delegated to agencies within those states.