when the tanker remembers to ask, we will provide them our tails (HC/MC/KC-130). Not sure what form they document the HAAR on, but our FE just writes it in on the refueling log on the back of the 781H (or whichever 781 it is where MX signs the ER). With HAAR, there doesn't seem to be a way to really have a precise quantity. I've had the tanker set their system to cut off after 500 lbs, and it doesn't, or it does, when we show an onload of less than 500 lbs. So we typically write what we saw for onload, and that's about it. I'm sure many times the offload number noted by the tanker doesn't exactly match...
I once HAAR'd where all the fuel was venting straight out of the pod into the atmosphere next to our aircraft instead of flowing through the hose to our probe. Their offload definitely didn't match our onload on that one.