Peel, halve and seed papayas. Cut into large pieces. Combine sugar with 3/4 cup of of water and bring to a boil. Reduce heat and simmer for about 5 minutes. Remove from heat and let cool.
Puree papaya with lime juice and sugar syrup. Place into a shallow dish and freeze for at least 4 hours. Stir with a fork every 30 minutes.
Scoop with an ice cream baller and serve.