In Argentina, the phone number is just the Airport's number. The service is ran by a local company named Manuel Tienda Leon. Some months ago 5 of us (family) travelled in EK J and were picked up by a VW Jetta, Citroën C5 and a VW Passat (old model).
On the return, an EK agent awaited for us right after we left the plane and told us to go to the Manuel Tienda Leon place after migrations and customs.