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Remove the pinion nut using either and impact wrench or breaker bar and a 1 1/16" socket. The pinion gear will slide out from the inside of the housing.
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Bearing separator set up behind the pinion bearing.
  1. Using a dead blow hammer, hammer on the underside of the bearing separator until the bearing slides off. Remove the crush collar and shim. You could also set up a two jaw gear puller to pull the bearing off.
Measuring the stock pinion head and shim with a dial caliper.
  1. Measure just the head of the new pinion gear with the dial caliper as above.
  1. Take the measurement from step 2 and subtract it from the measurement in step 1. Select the shim of the same thickness as the subtraction.
  1. Slide the shim of the calculated shim over the new pinion and take a dial caliper measurement again. Make sure that the measurement is the same as that from step 1. If it is not the same change the shim thickness until the desired result is achieved.
When we install the pinion and carrier into the housing we will used gear marking compound to ensure that our pinion depth is correct. If it is not we will reshim the pinion at that time.
To Illustrate With My Measurements:
The measurement of the old pinion with .030" shim was 1.911"

The measurement of the new pinin with .030" shim was 1.909"

As a result of these measurements only being off .002" I started my initial installation reusing the old pinion shim. This does lend some credence to those that have decided to reuse the factory installed shim from the very beginning. 
Note that in the end I used an additional .010" shim in order to obtain the correct pinion depth measurement and wear pattern.   But again, I did not know the history on this rearend when I started the project and it had 3.27 gears in it already, so I'm unsure of whether or not these gears were factory installed or installed by someone else.

In addition to measuring the pinion head I did include one other measurement. Since I was using a new pinion bearing and race I took a thickness measurement of the old bearing and race and compared that to the measurement of the new bearing and race.
The old bearing and race measured to be 1.040", while the new bearing and race measured 1.043". Since these measurements were very close I did not have to adjust my shim thickness to make up for a difference. If these measurements had been far off I'm not sure if I'd have added or taken away a shim from the pinion right away but I would have had that in the back of my mind when checking the wear pattern with the gear marking compund.
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Carrier Bearing Removal