White smoke comes out of exshaust

the turbo your mechanic put on was 2nd hand and knackered i expect ,,,,white smoke means turbo still gone ,,,,

The white smoke you are seeing is steam. From your description, sounds like you have coolent seeping into the combustion chamber, mixing with your fuel/air, and exiting out through your exhaust as steam. 1, blown head gasket. 2. cracked head or block, 3, warped head due to overheating. Most common is #1.

White smoke comes in two forms

On start up it can be unburnt fuel

While driving vehicle, motor warmed up ,
it is coolant in the exhaust,usually a bad head
gasket

If your bmw has a turbo,then a problem there,
from motor oil associated with turbo problem

this case , you have to check turbo charger , when high RPM white smoke means lubricate oil goes to engine so give white smoke . on low rpm trubo close coming black smoke means no enough air gose to engine so this need to replace turbo . some type of turbo can be clean the wase gate ( which open with diafam beside turbo) make sure it's moving when accilerate. check vacum is ok . then clean wase gate > only some type have wings inside )if no replace turbo

This sounds like you have a seal that is failing under the stress of high engine and turbo rotor rpm's, the white smoke is oil burning, either in the exhaust stream or it's oil getting into the intake stream and being burned with the fuel..
You can remove the turbo yourself but you may not be able to locate the issue.
I would advise that you take the vehicle into a turbocharger specialist..

White smoke is usually coolant, oil is usually a blue color, most turbos r cooled by coolant so U may have a coolant leak in the turbo, may B a seal or crack in the turbo. Check your coolant level occasionally to C if it drops.

Symptom: White smoke or water vapor from the exhaust. You notice white smoke coming from the exhaust when you start your car. If it is cold out, this may be normal. If the smoke does not disappear after the car is warmed, you have a problem. Possible causes:

1. Transmission fluid may be entering the intake manifold through vacuum modulator.
   The Fix: Replace vacuum modulator
2. Cylinder head gasket(s) may be bad.
   The Fix: Replace cylinder head gasket(s).
3. Cylinder head(s) may be warped or cracked.
   The Fix: Resurface or replace cylinder heads. (Resurfacing is not a DIY job)
4. The engine block may be cracked.
   The Fix: Replace engine block.

This is probably just condensation in the exhaust, if you are not loosing coolant that would be me guess.

you have a blown head gasket you need to get it to a shop as soon as you can

White smoke usually associated with water or moisture. it doesn't take too much water to produce white smoke. check

1. cloudy oil under oil cap
2. leak through gasket from cooling jacket to combustion chamber