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Ivars is actually a Spanish surname as you will observe at http://www.infobel.com/en/spain/. It's found mainly around Valencia and comes from the placename Ivars which you can situate at http://www.mapquest.com/maps/map.adp?formtype=address&country=ES&addtohistory=&address=&city=ivars&zipcode=. As you mentioned, it's thought to have a Basque origin, namely ibar 'bank, shore, valley'. If you go to http://www.geopatronyme.com/cgi-bin/carte/nomcarte.cgi?numero=0056226&periode=1, you'll see that there was a migration to France in the 19th century and that the name is quite common there now.