Place potatoes in a saucepan with enough water to cover. Bring to a boil over medium heat, and cook until tender, about 8 to 10 minutes. Remove from heat, drain, and run under cold water to cool. Drain well.
In a large bowl, mix together the potatoes, celery, onion, mayonnaise, and anise seed. Season with salt and pepper to taste. Refrigerate until cold. Garnish with sliced hard-cooked eggs, and dust with paprika, if desired.