can somebody explain me what is that??seems my mechanic forget to put it back after took it in for some check...is this the reason why my car power is cutting off on hard pulls?

 

Crankcase breather hose heater. It does not cause the problem you're having if the electrical connector is disconnected. If the hose is disconnected, the car will still run fine but you're now sucking in unfiltered air and potentially dirtying up your engine.

 

my mechanic told me that this is working on mini jcw engine and because i put a jcw engine on it without the jcw ecu the programmed the old ecu like the jcw...but im not sure if this does not infect my engine as there is not the plug and the wire for the connector

 

I really don't understand the big picture here. So you did an engine swap with a JCW engine? If yes, the ECU does have different programming compared to the S model

 

How about a picture closer to the part and not from the side.

 

i post a new photo with the part that i dont have complete on my mini and i think that this is causing my mini throtle response and lag i have exactly the same tube and i think something is missing

 

yes i know but both engine models have on the turbo mass high flow intake hose a connector which i dont have and i think it makes my throtlre responding not as fast as before