Trying to figure out what the black Hose with the "T" splitter is. One of the splitter is broke a I want to replace it. Any help would be great as I can't find anything about it. It connects there on top as well as into the intake under my Supercharger ** not my engine but similar***

 

The first step would be to tell us the year and submodel of your car.

 

That is what gives pressure to the fuel pressure regulator.. Down is the actual FPR, left goes into the LIM (i believe) into another T then around the back to the pressure sensor.

Heading to the right it goes into boost bypass solenoid. Then there is supposed to be a larger tube going from the solenoid into the boost bypass valve (the round black thing with the flapper) It seems you (that picture) are/is missing that part.

To simply answer your question, its the boost/vacuum line that connects all those things I just mentioned..

If its not your actual engine than this may not be of any help.. The 3800 and supercharged 3800 have very different vacuum line setups.. Cause you know, ones not just vacuum.

If yours isnt this exact (l67) engine, you will have an L fitting going to your fuel pressure regulator.. Theyre known to crack and its better to just replace with better materials.