This shouldn’t be happening in the first place. My first instinct would be that your not compositing your passes correctly or you have issues with your textures/alpha channels in the renders themselves. Without seeing the renders it’s hard to say. But if your rendering on black then you should be able to drop your renders on top of any background and not get white edges. To me that screams of incorrect compositing. If you can show examples that might help us figure out whats going on.
Tim J