Octavian and the Death of Anthony and Cleopatra

When Octavian conquers Egypt, one of the dilemmas that he has after the death of Anthony and Cleopatra is what to do crudely put with their children. So can you fill in the story at this point? I think Anthony andCleopatra have three children and then their Caesarean, Cleopatra's elder son. Plus a couple of Anthony's sons don't fare entirely well, I believe. What do the records tell us about the fate of Anthony andcleopatra's children?