I found one in my tank once. Cleaned the heck out of it and I've not seen any since.
Totally aside, but in my high school biology class we did an experiment with them. (Something I wouldn't do now, as I'm considerably more conscientious these days..) Basically what you said is true. You can chop a planaria into tiny bits and it'll make new ones from the bits. My lab partner and I sliced our worm's head in half so that it had two heads. (I feel awful about it now. ) But they are really, really resilient creatures, and they're pretty amazing. There are some other experiments that psychologists have done with them. They've conditioned them to associate light with an electric shock, then chopped them in half. The *tail* half automatically knows to avoid the light to avoid the electric shock! What the heck?? Stuff like this raises huge questions about the nature of memory and the mind, all from a lowly worm....
Anyhoo, good luck with the battle at hand.