Well, I'll give it a try.
The centre differential uses wet clutch plates with an external electrically operated actuator (which applies the clutches) to divide the torque front/rear. A control module montors wheel speed and controls the actuator. Torque is 40/60 front/rear (from memory), but will vary from that depending on measured slip front or rear (using the ABS wheel speed sensors)
The above varies from earlier (non x-drive models, prior to 2004) that don't have clutch plates in the center differential, but rather just an open center differential.
At each of front and rear there is an open differential in the axle, with no mechanical anti-slip function. All side to side traction control is achieved via brake application on each wheel, through the DSC (Dynamic Stability Control) system, which includes traction control.
There are further systems that manage vehicle stability and can apply an individual brake, but I would refer to those stability systems as opposed to traction systems.
The BMW training materials from when the E70 came out in 2007 covered this. Read through this link for more information on the E70 powertrain.
http://www.bmwmotorsports.org/pdf/e7...Powertrain.pdf
The following link includes information on Longitudinal Vehicle Dynamics, which covers the use of brake application to increase traction. Note that BMW refer to it as Automatic Differential Brake, but that is the effect it achieves; it actually works by applying a brake on a single spinning wheel.
http://www.bmwmotorsports.org/pdf/e7...%20Systems.pdf20Dynamics%20Systems.pdf
These and more are available under the section titled Online References at the top of the page. Select PDF, then E70.
Jeff