Get out the owner's manual or look it up on line through GM Manuals. https://assets.gm.com/manuals/hummer..._h3_owners.pdf

When the T Case is locked, you have locked the front and rear axles together, got nothing to do with wheels. Traction control will spread power to all the wheels sending most of it to the wheel(s) that have the best traction, might be the left or right depending on whatever obstacle and surface condition you are dealing with.

 

Makes sense. I forgot about traction control playing a part in the equation.

Will traction control help when the vehicle is stationary and one wheel is spinning?
With the transfer case in lock, the other axle will help get it moving but with regard to an individual axle i don't know if traction control helps. Normally with an open dif a spinning wheel causes the other wheel to be bypassed and receive no power. Traction control will apply the brakes and slow the spinning wheel. This is great when the vehicle is moving as it can synchronize the two wheels and apply power to the other wheel. But even if the traction control stops the spinning wheel on a stationary vehicle I don't know if the other wheel will come into play. You have all seen a "one wheel peel" from an open diff as the result of applying more power than the friction can hold.