So here are the basics:
You “own” a domain name by having it in your account at a registrar.
1) The public who-is information on who owns the name, or set privacy.
2) The name-servers all internet traffic worldwide are directed to for your domain name content, email and files.
3) You have the exclusive annual right to renew the domain name, you can pay ahead as many years as you choose, at any time.
4) Should you choose to sell these rights to someone else, you move the name form your account to their account.
5) You can choose which registrar will hold your name by registering at the registrar or hosting company of your choice, or transferring a domain name form one registrar to another.
The registry control the records of which registrar holds which name for each customer, and makes sure that only one person owns each domain name, and report to registrars if a name is available for sale, or taken.
In .LA, there are also premium domain names for sale. These names have market based initial price, and then renew like any other .LA domain name. See premium names here at VIPDomains.LA