The paper towels will absorb the excess moisture, and the ricotta will peel right off. The baked ziti can be prepared through step 4 up to one day in advance and stored, covered, in the refrigerator.
Stir the sauce, 1 cup mozzarella cheese and ziti in a large bowl. Spoon the mixture into a 2-quart shallow baking dish. Sprinkle with the remaining mozzarella cheese and Parmesan cheese.