In my neck of the woods, Blackwater provided what was basically a PMT to finalize training of Afghan Border Police, including actual work in the field. One brigade commander welcomed their participation and in an AO suffering from severe manpower and asset shortages, they filled a vital role in actioning our intel (that is, they were the only entity in our battalion AO that could/would move on time sensitive targets). The mentors seemed to make sure the training was adequate beforehand that they could mostly hang back and let the ABP officers do the op with limited interference, offering advice or guidance where necessary.

After a new brigade RIPd in with a more... risk averse commander, the Blackwater mentors were essentially confined to their remote COP and only allowed to hold that ground. From what I hear, 4th ID had to do a lot of clean up after they replaced that brigade due to the inaction of a year...

I don't know all the details of what exactly their contract dictated, but they seemed to fill the mentor role without serious incident. As far as command and control, the AO commanders were still in charge with USFOR-A elements often providing communications support in case air or other assets became necessary.