Here's a chair from Charlotte Friis Design Studio that's made out of drawing paper rolled up like a pair of toilet rolls, and as a child uses paper, it's scrolled from the back roll to the front one on which the child sits. As the child uses more paper, the chair gets taller and taller, conceivably getting larger as the little tyke grows taller.
If you're familiar with the propensity of the wee ones to draw for hours on end—sometimes in places where they shouldn't—you'll realize how much they'll like something like this. There's about 1500 feet of paper in that roll, enough to be changed twice a week for five years. Pricing or availability was not mentioned.
Children's Paper Chair [Cool Hunter]