When Does A Friend (ex Friend Now) Staying On My Couch Become A Tenant, With Tenants Rights?

Does he have a key and does he receive mail at your occupancy?  If yes to either...you must evict him and the police will not help in removing the couch potato...sorry.
The only way out of it is if your lease states who has permission to live there...though this scenario may be grounds to evict you both!  I am a paralegal and see this all the time.

He is right about the eviction, but "only" if you have allowed him to receive mail at your address. You can check this out by calling your local police department.
I don't know if it is the same in all states or countries, but in the state of Florida in the USA it is a law. If it is so in your area, you can most likely just go down to the courthouse and pay around $100.00 to have the eviction papers served on him.