Sponge... We have what appears to be the same kind growing in our tank. Ours appears to have actually grown through a hole that goes completely through one of the pieces of rock in our tank. It's real small on the one side, pretty much just enough to stick out of the rock (only a large hole on this end), but is growing up and out the other side like a tree, where there are other noticable holes in its structure every so often. I call it white tree sponge, but there's undoubtedly a better, more correct name for it.
It will also start growing in other parts of the tank if a piece gets broken off. I accidentally tore two small pieces off it a little while back, now those two pieces have started growing elsewhere in the tank where they settled.