It is basically the anethole (a phenol) of the star anise that react with the sulfur in the onion to create sulfur-phenolic aromatics. In Chinese cuisine the same family of reactions is used with duck and pork.
The sulfur-phenols are also produced during the Maillard reaction, the reaction that gives grilled meat its characteristic flavor, so adding star anise to the onions will give your dishes more of that grilled, browned flavor. The reactions of the compounds in the star anise with those in the meat are not the relevant reactions for flavor or texture.
From averaging a few recipes, I would say 1 star anise for every 250g of chopped onion. Too much star anise will highlight the other aromas in star anise, so one has to use it in moderation and allow enough time for the reactions to take place.
Garam masala, a common Indian spice combination that is used in meat dishes, may have star anise. Star anise is sometimes used in French onion soup — it intensifies the caramel flavor of the onions — and in Vietnamese cuisine, which today incorporates French elements.