ST and *A are equally strong in Europe and the USA right now. Should CO actually make the leap to *A (and it is not a done deal yet by a long shot) *A will become stronger in Europe/USA based on the benefits that CO takes away from ST and moves in to *A. For Asia the change means nothing. *A remains strongest, followed by OW and then ST. For Africa the change means nothing. *A is probably strongest now thanks to EgyptAir joining and giving more options than just SAA. ST is second with KQ and then OW. And in Oceania it goes OW/*A/ST.
Really very little will change, but ST will still trail in most regions. The fact that most the people who fly live in the USA/Europe means that ST likely isn't really all that worried, but that's a whole different part of the discussion.