You might need paper for this one...
FIAT (the cars), FIAT Professional (the vans), Abarth, Lancia, and Alfa Romeo are five separate companies, owned by a holding company called "FIAT Group Automobiles S.p.A" ("FGA")
FIAT Group Automobiles, Maserati, and a company called FIAT Powertrain Technologies (FPT) are in turn owned by the "main" FIAT holding company, FIAT S.p.A. FIAT S.p.A also owns 90% of Ferrari, 60% of Chrysler Corporation (Jeep, Chrysler, Ram, Dodge) and a collection of components and robotics companies in the carmaking business (Magnetti Marelli, Comau and Teksid). [ there is another FIAT holding company, FIAT Industrial S.p.A, but that has no carmaking businesses, so it doesn't come into this discussion ]
So, as a part of this larger group, Alfa and FIAT develop their own models using shared platforms or architectures developed by their parent company FIAT Group Automobiles, in whose factories the cars are built. The engines and drivetrains are developed and manufactured by FGA's sister company, FIAT Powertrain Technologies, which sells not only to FIAT's brands, but also to other carmakers (this is why some Suzuki and Opel/Vauxhall models have FIAT diesel engines in them).
Maserati builds the Alfa 4C for Alfa Romeo at its factory in Modena, but Alfa's other cars are built in FGA plants: Cassino in central Italy for the Giulietta, and Mirafiori in Turin for Mito. Before being bought by FIAT, Alfa had two major factories: on in Milan (Arese) and another near Naples (Pomigliano d'Arco, formerly known as the "Alfa South" works, and that's why the car was called "Sud"). Arese is closed down completely, and the factory in Pomigliano now builds the FIAT Panda, and is considered to be one of the most advanced in Europe (a far cry from the days when it was building the Alfa Sud!).
So in summary, everyone makes stuff for everyone else these days.