Combine first 3 ingredients and 5 quarts water in a 12-quart covered stockpot.
Bring to a rolling boil over medium heat.
Add potatoes and sausage; cover and cook 10 minutes.
Add corn; cover and cook 5 minutes.
Add shrimp and crawfish; cover and cook 2 minutes.
Remove from heat. Let stand, covered, 10 minutes.
Drain. Serve with cocktail sauce, tartar sauce, and hot sauce.
