Blow this out to include any social media site: if some facebook or twitter group becomes sufficiently popular to the point of being able to market/capitalize o

Blow this out to include any social media site: if some facebook or twitter group becomes sufficiently popular to the point of being able to market/capitalize on that popularity do the respective hosts have any claim to take over those groups or get a cut of the product? If I rent space in a strip mall, don't I pay my landlord a fixed rate no matter how much money I make? Can he kick me out at any time and basically take over the product/brand?