Most sponges, like most corals, just kinda keep growing. There are cloud sponges in our waters (okay..a little farther north..Washington and BC) that are as big as VW's and tropical barrel sponges almost as big.
I've found that most of the "hitchhiker" variety sponges that survived transit and set up shop in our systems at work prefer the underside of ledges, like the little guy under your palythoa and they continue to grow only in the shaded area, clinging fairly closely to the rock. That being said, there are many, many different species of sponge, so YMMV.
On the competition with corals note - sometimes they certainly can overgrow coral colonies and more - many of them compete through allelopathy (the release of chemicals into the surrounding water that inhibit the growth of or kill other sessile invertebrates). Again..probably a rarity in captivity to experience any detriment from this, but it's always something to keep in the back of your mind, especially if you're in a smaller system where the allelopathic chemicals can build up more quickly.
Cheers,
Austin