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RE: What's the thickness of a continuity plate

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I was designing an ordinary beam-column moment connection. 
> I used a 3/4" thick cover plate, and the thickness of the beam 
> flanges is 7/8".  My calculation indicates that the use of continuity 
> plates is just barely needed; nevertheless, I chose to use continuity 
> plates whose thickness is the same as that of the beam.  When 
> my supervisor examined my calculations, he said that the thickness 
> of the continuity plate has to be equal to the total thickness of the 
> cover plate and the beam flange. 
The initial recommendations (i.e., right after Northridge) had that total thickness idea in them. It was soon learned that this extreme and expensive stiffener thickness was not needed -- and might involve such large welds that it would create other problems due to the shrinkage of those welds.
In addition to the information in AISC Design Guide No. 13, which David Williams was kind enough to point you to already, you can find a lot of information on what stiffener thicknesses were used in actual tests for the SAC Steel Project in FEMA 350. That and the other FEMA documents can be obtained on the AISC web site here:
You'll find that the stiffeners recommended now are generally a lot thinner than the first blush recommendations -- and can even be eliminated entirely in some cases per that testing.