Combine the masarepa, warm water, anise seeds and sugar, mixing thoroughly. Let mixture stand for five minutes.
Knead with your hands for about 3 minutes, moistening your hands with water as you work.
Form 6 small balls with the dough. Place each ball between 2 plastic bags and with a flat pot cover, flatten to ½ inch.
Heat the vegetable oil in a large heavy pot to 350 F. Add the arepas in the heated oil one by one, fry for 3 minutes, turning over once about half way through.
Using a slotted spoon, carefully remove the arepas from the oil and drain on paper towels.