We've seen both. Had one offer presented from the RC over the phone when they knew it would be a while until we could get to their campus. Another offer was from the RC immediately after we met with the HC. 2 others were delivered from the HC.
Along those same lines, each offer was broken down differently too. These are not actual #'s from the offers but examples. Two schools broke their offers down by what was covered and not covered - tuition, books at 100% but no meals or housing for example. One school gave a % that was covered - we'll pay 56% of everything. One school gave a $ amount plus books - total cost of attendance is expected to be $25K and we are willing to give you $10,000 plus books.
Bottom line - every school handles it differently so ask questions to clarify.