So i registerd a domain name with a company. They say its free due to the fact i pay a monthly hosting fee ,but is it free . Do i own it out right. Will they have the right to terminate after a year or 10 years when i grow my company?

Different hosting companies have different practices.
Read the Terms and Conditions carefully.

Do i own it out right
Ask them
Best, do a "whois" to see if YOU ARE listed as the registrant. and NOT them

Will they have the right to terminate after a year or 10 years when i grow my company?
You mean they snatch your name.
Possible...
If they are the registrant!!

check!!

This may sound pedantic, but nobody owns a domain. You don't buy a domain, you register it. You are not the owner, you are the registrant.

The registrant is the person with the legal rights to the domain. You need to check the Whois to find out who is listed as the registrant. Any ethical hosting company will register the domain in their customer's name, but there are some unethical ones around that will put themselves as the registrant.

Originally posted by Lubeca
This may sound pedantic, but nobody owns a domain. You don't buy a domain, you register it. You are not the owner, .... I overlooked this point:)