Euros only! Atm's, banks, you name it!
However, you'll still see prices (in spain especially) still with the pesetas quantity everywhere. People have been using pesetas for a lifetime and its going to take awhile to transition and adapt entirely to seeing prices only in Euros. I don't know how long they plan to do that, but my guess is it will be awhile.
But don't worry, everything gets paid in euros now. If someone tries to exchange you pesetas, you're getting ripped off! Technically except what people may have kept for a keepsake, you shouldn't be able to get pesetas from anywhere!
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Madrid!