Rear end locks up when in 2wd. Each time this happens the back right wheel binds-up as though the break is on hard. This happens only on occasion, each time it has happened when moving very slow and making a right hand turn onto a slick surface. This happened before and after the transfer case being replaced.

SOURCE: rear brakes lock up

Not wanting to be too general but at least trying to help I would suggest looking under the back end, and specifically at the rear backing plates and to the insides of the rear wheels, to see if you notice any fluids dripping. If these are drum brakes, then you could very well have either a wheel cylinder leaking brake fluid, causing the brake shoe linings to swell up, or it could be a leaking axle seal, allowing differential gear lube out, which will also cause the linings to swell, and minor braking will cause that particular side to lock up.
If this vehicle has rear disk brakes, or was just recently changed from rear drum brakes to rear disk brakes, it is possible that the proportioning valve in the brake line was not changed to match with the disk setup.
Drum brakes operate at approximately ten pounds per square inch pressure (10 PSI) whereas disk units operate at a lower pressure of about 2 PSI.
Just some things to look at. Some brake fluids have no smell, others are very distinctive in odor, and differential gear lube has a very distinct odor...not hard to miss once you've smelled it.

SOURCE: steering problems with my 98 Chevrolet k1500

There is a unit in the steering column called a steering speed sensor. Replace it and all is well. I had to do it on my 1998 Chevy at 140,000 miles and all is good. Have since done it on another 1500 and it corrected its problem too.

SOURCE: Transfer case leak

You mean between the case halves? It is just silicon, no gasket. These are good for the pump wearing a hole in the rear housing and leaking oil. The cure for it is a new rear housing and a piece called a case saver that keeps the pump from doing it again. Taking the transfer case apart to fix it is easy, I can tell you how to do it.

SOURCE: Rear end in 1999 chevy 1500 binds on turns

well i had the same problem everyone told me the clutches in the rearend were sticking making it stick in positive traction (only your passanger side rear wheel pulls unless you start spinning then a type of clutch engages the other side so you have traction then when you stop spinning it disengages it should never be engaged if your on pavment) now you can do what i did listen to everyone when they tell you its normal or you can take it to someone with experience now and save yourself some money cause it will start popping then it will get some viberation then next it will break the clutches and when that happens you will have to replace the pinion,ring,and the spider gears as well as the clutches.make sure you have pleanty oil in rearend if you dont add the limited slip conditioner it might free clutches up but if i had it to do over id put it in the shop or stop driving it before i broke something hope this helped

SOURCE: rear end noise and seizing now

Sounds like one of two things is happening
1). the spider gears are binding
2). the ring gear is binding on the pinion

Check the pinion gear bolt for tightness first, then check for excessive end play. Make sure you have the correct fluid for your rear end type (limited slip takes one type, semi-posi takes another type and even sometimes reguires an additive) Hope this helps.