1 Boil sugar with 100 ml (approximately 1/3 cup) water for 1 minute, then allow to cool. Squeeze juice from lime.
2 Mix together coconut milk, sugar syrup, 2 tablespoons lime juice and the pineapple juice.
3 Pour juice mixture into a shallow baking dish and place in the freezer until it starts to set around the edges, about 4 hours. Continue to freeze until solid, stirring vigrously with a fork every 15 minutes, until the texture of granita. Store in the freezer until further use.
4 Peel mango, cut into slices around pit and then dice flesh. Peel pineapple, cut into quarters and remove core.
5 Peel papaya, halve, remove seeds and chop flesh coarsely. Peel tamarillos and cut into wedges.
6 Mix together 2 tablespoons lime juice with the rum, then mix with the fruit. Let macerate for 30 minutes. Serve fruit salad with granita.