Can I make an adult child leave my home if they are living there without paying rent or other fees

Yes, simply evict them.

Anyone leaving in your home is a resident, no matter what their family status. They need to be evicted according to local laws.

Homesteading in my state anyway means the right of immediate family to stay on after the owner dies until the estate is settled by probate court. Nothing like your situation, but many people think they have more rights than they do have.

The definition that Joypulv described may be accurate in her state, but in general the word has several meanings, none of which pertains at all to OP's situation:

• An old Federal statutory program, repealed decades ago, by which people were allowed to acquire title to land by living on, improving, and farming it.
  
• Claiming a certain amount of land for a partial tax exemption, exemption from execution, etc

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... in general the word has several meanings, none of which pertains at all to OP's situation:


And lots of people use it today to mean living off the grid.