What is the process for evicting a relative (child over 18 or other adult family member) who does not pay any rent nor has any ownership rights. You just want them out of the house.

This depends on your area. Some areas would just allow you to pack up their things and place them outside then change the locks. Others would require a formal eviction process.

I would give them a time frame to move out and warn them if they aren't out by then, you will pack up their things and put them in a storage facility for which they will be billed.