Should I allow existing tenant to stay/how does it work?

[Eric Lin]

I'm purchasing a property with an existing tenant who has expressed a desire to stay. I'm very new to this; how does this work?

- Do they sign a new lease with me or does their existing one transfer? If the existing one transfers, can I still increase the rents? Their rent is currently below market price. 
- How is the pre-inspection done. Since they have a lot of stuff in the house already, it's hard to determine accurately the state of the house which will be needed when they move out. 
- Should I still run the background check and everything on them/process them as a regular applicant? They're a family of four children so I prefer to not uproot them. 

Does anyone have experience with keeping a tenant after purchasing a property? Recommend or no, and for what reasons? 

Thanks!