Take, for example Nextel (which I currently find most attractive for my needs, but the question is not limited to this particular operator). According to this one must register the new "line" and here it is stated that National Identity Document (DNI) is required. I recall that my friend, with whom I traveled last year, had to go through hoops, maybe even involving using DNI number of a local friend – I do not recall the details – to register the prepaid SIM (I do not know which operator that was).
I plan a 40 day stay in C.A.B.A. and would really like to have reliable mobile internet. This is my second visit, and I know that occasional WiFi hotspots are just not going to be enough for me.