under STAR you find everything you want to know. Here just very brief: no matching of the current one-world-offer, but it seems that a dicounted eco-rtw-Star-rtw offer (StarLITE) is just on it's way to be offered.
The last StarAlliance bonus promotion I know was running jan-feb-99 ONLY by LH: the more different Star-carriers (no code-shares) you did fly during that period and got credited to your LH-miles&more-account, the higher your bonus (fly them all = 50'000 miles bonus). UA had a similar promotion running late 98.
With Star rtw-fares, you can (and I often do) enter different ff-programs for each segment for which you get a different boarding-pass. Two years ago, in late 97, UA and LH did run their first StarAlliance-promotions simultanly, and the bonus for riding all partners then was higher (100'000 miles). With one rtw-StarAlliance-ticket (my very first one) I did then 2 segments with each carrier (and per carrier one segment creditet to UA, the second one to LH) and I made a total of 200'000 bonus miles plus the actual flight-miles and status-bonus.