Sandy - I use parchment paper about 95% of the time on my baking stone. I don't cut it into a round as I have a rectangular baking stone - so I just tear off a sheet of parchment paper that is large enough - and put my crust on it - fill it - slide it into the oven and have never had any trouble. If your baking stone or pizza stone is small - you would NOT want the parchment paper to overhang the stone more than a wee bit .. as it wouould scorch. I doubt it would catch fire.

I've done this for 4 - 5 years mainly because it did sometimes stick to the cornmeal .. and also because the cornmeal would dust off into the bottom of the oven and I'd have to put it on clean a lot more than I wanted to!

I use the parchment paper whenI'm making bread, rolls, cookies --- most things. I should buy stock in their company! Occasionally I can re-use the paper 2 - sometimes 3 times. Not always as I'm a messy cook!

Good luck