Tiene un intercambio de acciones en Air Berlin (cada una de ellas posee un 10% de la otra) y opera algunos vuelos para ésta.
German airlines use to include this kind of chart showing flights and destinations in their timetables.
TUI fly (info Wikipedia) is the direct succesor of German carrier Hapag Lloyd, which for some time splitted into two airlines, Hapagfly and low cost carrier HLX.com. Now, all flights are operated by Hapag Lloyd trading as TUI fly. They fly both charter flights and as a low cost carrier.
TUI fly has a 10% share exchange with Air Berlin and flies some flights on their behalf.
TUI airline management