If you 'sponsor a child', what happens to the kid next door?

So, I am watching tv and see the commercial with the old dude wanting to jerk my heart strings enough to send money. I could sponsor a child and they show a really cute kid standing in a doorway. Let’s say I do what they want, what happens to the kid next door, or down the street? Or for that matter the parents? What if they are all hungry also, what does the charity do? How do they pick a kid from five thousand?