car is still coughing out black smoke sometimes when I pull away from the light or on the freeway when I have to slow down for traffic and then give her some gas, I have replaced the blow off valve and even the throttle body with no luck....I need this fixed

Thanks for the update. Congrat's on fixing the problem!

So after I went through the engine again.... the intake cam gear was bad, spring inside was broke, so the cam gear turned whenever it wanted to, so I replaced it and the car runs great

116 000 miles on her, and yes the engine was a complete failure, timing chain broke, cam bolt broke, turbo and cat were not replaced, I have about 200 miles since rebuild and the turbo feed line was not replaced but taken off and cleaned and air blown through it, and now I was getting a code for intake cam sensor, so I took off the valve cover and saw that the intake cam was off 1 tooth, I fixed that problem and now it wont start....

I have some questions to better understand the circumstances:

How many miles on the car (to understand the condition of the cat)
What was the reason for the engine rebuild - catastrophic failure or general high mileage (same reason as above)
Was the turbo and/or catalytic converter replaced or refurbished?
How many miles since the rebuild?
Was the turbocharger oil supply line replaced?

It being a computer-managed engine, I'd check the connections to the air flow sensors and the like and that they are functioning properly. If they don't sense what they expect in terms of air flow and exhaust O2 readings, the confuser could be dialing back (or up) the spark timing, the amount of fuel injected and perhaps the waste-gate management (not sure if it is computer-managed). Maybe even throttle position.
What you feel as lack of boost may be engine lag. The puff of smoke suggests an over-rich condition that the engine eventually coughs out.

A loose hose or something leaking out air pressure?

the turbo on my 07 mini is not working all the time, and sometimes when I pull away from a traffic light it lets out a huge plume of smoke, engine was recently rebuilt by me, what could be wrong with the turbo ?