When a rear axle is said to be welded to make it a posi, what exactly in the differensial is welded? I read an article a while back that talked about filling in every other tooth on the spider gears with a weld, but don't remember reading any thing about how well it worked.  

You can weld the spider gears together and or to the case. When it breakes you will need to pull both rear axels to get home so you will need a full floater rear axel for this to work unless you can figure out how to support the rear of the rig with no tires.  

weld the spider gears to the side gears.If you want it stronger,weld all that to the case  

Why would it be necessary to remove the axles if the diff breaks.I've never came across this problem.