This paper evaluates whether 1) protoplatyrrhines could have migrated to South America via Antarctica, and 2) the floating island model is a plausible transoceanic mode of dispersal for land vertebrates like protoplatyrrhines. Results show that Eocene Antarctica and Australia supported large and dense forests, and that the Antarctic fauna was comprised of many species of vertebrates, including placental and marsupial land mammals. However, no primate remains have ever been reported from these continents. Antarctica and South America were connected until the Middle Eocene (i.e., after the oldest Asian anthropoids), but two major water barriers existed between Antarctica and Asia since the Early Eocene. The Eocene and Oligocene water gap separating Africa and Antarctica was excessively large. Thus, all scenarios involving an Antarctic route have been rejected. The African scenario is difficult to falsify because only one water barrier existed, both paleowinds and paleocurrents were favorable, and Paleogene African anthropoids show phylogenetic affinities to platyrrhines. I tested whether a journey on a hypothetical floating island over the Paleogene Atlantic Ocean exceeds the survival limit of a genetically viable group of animals such as protoplatyrrhines. Studies of water deprivation suggest that they could have been able, with a body weight averaging 1 kg, to survive without water for at least 13 days. I have used the present Atlantic Ocean as a model for the velocity of Paleogene paleowinds and paleocurrents. Considering winds as the key accelerating force of floating islands, the Paleogene Atlantic water barrier could have been crossed, in the most conservative scenario, in 8 days at 50 Mya, 11 days at 40 Mya, and 15 days at 30 Mya. In order to survive a transoceanic journey, however, protoplatyrrhines had to be preadapted to strong seasonal variations in water availability in their original (African) environment. Once on the sea, their brains would have physiologically interpreted the rarity of water as the beginning of the dry season, and the group would have switched its diet to alternative foods, i.e., everything available on the floating island.