Well, there hundreds if not thousands of effects available for AE. Some deal with edge pixels in one way or another, others use a preview area to speed up the setup, others are demo's with various watermarks. You could have also applied the effect to an adjustment layer that was smaller than your composition. I haven't got enough time left in the day to give you a solution for all so if you cold just tell me what effect you're using and how you've set up your composition someone here on the forum could probably give you a solution that's only a click or two away.
I'm working with 3D light casting. I followed the tutorial here: http://www.videocopilot.net/tutorials/q/energy/ So I made my first composition that made the light, rendered it, then imported it back in another compostition along with my footage. The light was too big for my footage, so I scaled it down and moved it into the position I wanted. So the borders of the layer that it's in, is showing in my footage.
I'm guessing that you mean tutorial 93. 3D light casting. I spun through the tutorial in about 2 minutes and found the part where the energy ball was scaled.
Rendering out the energy ball and dropping it on top of you footage won't work. There's no way to scale rendered footage and extend the edges without mirroring, repeating, or duplicating the layer. You'd end up with a checkerboard which wouldn't work at all.
Try opening up the sample files and then replacing the background with your footage. Then go through the steps to line up the perspective and scale the energy ball appropriately. The key to selling this kind of effect is to match the perspective of your footage and throw in some foreground elements.
If you don't know how to replace footage just press F1 and type "replace footage" in the search field.
Thanks Rick! That did it!