I think we've all established by now that Germany, even with total air supremacy, could not have invaded Britain with its motley collection of river barges.
But I think there's one aspect of the story that we're all forgetting here.
With air supremacy, who needs barges? YOU CAN SIMPLY FLY TROOPS OVER THE CHANNEL!
Had they gained air supremacy, what if anything would have prevented a WWII German AIRBORNE invasion of Britain?
P.S. If we've gone over this before,just point me there with a link and give a short summary of why. DON'T flame me for not knowing of its existence.