Delta is the world's largest carrier in terms of flights per day and passengers carried per day (over 1/3 million each day) - and is the biggest airline across the North Atlantic to Europe & the Middle East. Altho it would be very good if it were to happen, it is extremely unlikely that BA would tie up with an airline bigger than the airline that is was told it couldnt.
IE Delta, being bigger than American, would be unlikely to be allowed to tie up with BA as there would be an even bigger monopoly across the Atlantic with Delta than there would have been with American.
Besides, Air France, Delta's #1 partner, is too similar to BA in terms of destinations & locations to be comfortable with its largest rival sharing with it. Not only this, but if the rumors about Virgin attempting to join the Delta/Air France group (I am unclear as to whether these rumors are true, however) then it is very very very unlikely as there aren't bigger enemies in the Commercial Aviation world than Virgin and British Airways.
And as to Star, I am afraid to say that I know very little about Star, so I am unable to comment.