The rights of non-owners to use portions of property for their own (stated) purposes granted by recorded owners are called:

The answer is easement.

Explanation:

Easement is the right for a person to use real property. This is a non-possesory right, meaning the person in question does not share part of the ownership.

An example would be allowing someone to walk across a piece of land in order to access his own property, or granting the right to fish in a private pond.