M.R.
Even if you only invite a specific child, it's my experience that some will bring themselves and their other kids anyway. It's sort of a pain! I'm always considerate about this sort of thing, because I've thrown my child large parties, had pizza, and the parents end up eating pizza and cake too. Seems rude to me, but its happened enough times to me that I assume this must be the norm. I always just buy extra food and goody bags just in case...and keep the guest list low.