We consider the following correlated percolation model on the d dimensional lattice Z^d, d >=5. From each vertex of Z^d, we start POI(v) number of worms (v>0), where the number of worms are i.i.d. for different vertices. Each worm w has a random length L_w, moreover the lengths are i.i.d. for different worms. Each worm w (independently of other worms) performs a simple symmetric random walk of length L_w-1 on Z^d. Let us consider the set S^v of sites visited by these worms. How do the percolation properties of S^v depend on the length distribution of worms? We give an easy sufficient condition under which S^v exhibits percolation phase transition and a more involved sufficient condition under which S^v percolates for all v>0. We compare our model to other known models (e.g., finitary random interlacements, Poisson-Boolean percolation model) and argue that the percolative behaviour of our model is quite close to being “extremal” in a natural family of similar models. Joint work with Sándor Rokob.