Without dominance, submission is meaningless, and vv. Why else are we all looking for someone, if it was enough to 'be' dominant or submissive by yourself? A Dominant allows the submissive to be submissive, to give her gift of submission to him. He facilitates it, allows it, accepts it.
But I don't think it's too fanciful to say the Dominant also gifts his dominance to the sub. If there was anything half hearted about it on either side, the whole transaction would collapse.
I always find it extraordinary - despite the seeming 'rules', strictures and disciplines of BDSM, we are actually freely giving each other a willing gift.