When to stop hilling up potatoes?

I've got potatoes growing in big garbage cans and in tires. I read that when they flower, you can begin to harvest little "new potato" size spuds. Does this mean that there will be no new tubers? If I continue to hill them up, will I foster new spudlets, or are what tubers there are now all I'll get for this season and they will just grow bigger? (I don't know if I am being clear in expressing my question.)