I don't know about leaving the country as we don't have any trips like that planned.
We recently bought a car at a Renault dealership without any problems. Don't take all the cash to the dealership. You take a reserve, for us it was 3000 pesos. Then we had a few days to deposit the balance, which we did in cash, to the bank account (the dealership will give you the details). Then we waited for a call that is was ready to pick up. You do need a CDI number from AFIP which requires a certificado de domocilio. Both were easy to get and we also only have tourist visas. Other than that just your passport. We decided to go with the insurance offered at the car dealership as a friend told us the rate was a good one. They did all of that for us and the process was pretty smooth. It was a little over a week though from when we gave the reserve to when we actually were able to pick up the car.
We recently bought a car at a Renault dealership without any problems. Don't take all the cash to the dealership. You take a reserve, for us it was 3000 pesos. Then we had a few days to deposit the balance, which we did in cash, to the bank account (the dealership will give you the details). Then we waited for a call that is was ready to pick up. You do need a CDI number from AFIP which requires a certificado de domocilio. Both were easy to get and we also only have tourist visas. Other than that just your passport. We decided to go with the insurance offered at the car dealership as a friend told us the rate was a good one. They did all of that for us and the process was pretty smooth. It was a little over a week though from when we gave the reserve to when we actually were able to pick up the car.