For reference, here is the order of things you need to do to depart EZE:
1) (Very Important to do this first) Get your "Tax-Free" (program for getting a partial refund of VAT when buying at certain stores) vouchers stamped - there is a seperate line for this. Because the person stamping the form may wish to see the purchased items to make sure that you are taking them out of the country (and haven't consumed them or given them away within argentina), you need to do this before checking your luggage. FWIW: I only saw one person required to produce the item.
2) Check-in with airline. For us (elite travellers on UA) this consisted of proving to an agent at the front of the line that I was a 1K, then a relatively short security interview by a security agent (did you pack your own bags, etc) where he placed sticker on our passports and "X-Ray" tags on our luggage. Finally we were in line to see the agent that would check our bags and give us BP's.
3) Go upstairs and get in line for departure tax. Stickers are applied to BP's.
4) Wait in line to show BP's and have tax stickers scanned (presumably to prevent re-use).
5) Walk a bit and get in security line. Security is interesting. Lots of armed agents, but looser procedures that in the US (no need to remove all that excess metal from your pockets, as no one cares when you set off the WTMD - in fairness the additional screening later on makes this fairly reasonable).
6) Walk a bit and get in line for immigration. There were two lines that begin next to each other but most folks would instinctively get in the first one not noticing the second one. The second one was a bit shorter.
Immigration took the exit half of the form we filled out upon entry, stamped our passports, and (I think) double checked the departure tax stickers.
7) Wind your way through the duty free mega-mall to get to the reasonably well hidden "Tax-Free" VAT refund booth. You will be given a choice of pesos in cash or USD applied to the credit card of your choice.
8) After doing any additional duty-free shopping or airline club relaxing, proceed to your gate where you will need to remove all metal objects from your person and undergo a thorough wanding including shoes (but no need to remove your shoes). You then take your carry on stuff a few feet away to be fairly thoroughly hand inspected, before being ready to sit in the gate area and wait for yuor boarding group to be called.