Map of Oceania showing Polynesian outliers. The red zone is the original Polynesian homeland, from where Polynesian seafarers went to the various Polynesian outliers. The lines around countries and territories are not the actual maritime borders.
Sources for this map : 
Original map : File:BLANK in Oceania (small islands magnified) (-mini map -rivers).svg 
Island names : 
Fidji : File:FijiOMCmap.png
New Caledonia and Vanuatu

File:Map_of_Efate_Island_EN.png
File:New_Caledonia_and_Vanuatu_bathymetric_and_topographic_map-fr.jpgSolomon Islands : 

File:Map_of_the_Santa_Cruz_Islands_(Solomon_Islands).png
File:Solomon_Islands_Regions_map.svg (used to locate Anuta and Fatutaka, hence their imprecise location on the map)Tonga: FIle:Tonga.jpg
Micronesia: File:Micronesia,_administrative_divisions_with_island_names_-_colored_-_fr.svg 
Marshall islands: 

File:MH_-map_A.pngKiribati :

File:Kiribati_map_LOC.jpg
File:KI_Phoenix_islands.PNG (I manually added Rawaki)French Polynesia : File:French_Polynesia_relief_map.svg

List of Polynesian Outliers : https://fr.wikipedia.org/wiki/Exclaves_polyn%C3%A9siennes
Own work
Skimel