This thread is 4 years old.Just because I happen to be looking for the same thing, and because I sensed an air of condescension on the part of Aeacus, I wanted to say that this is what the OP was looking for and they do have batteries and do, in fact, exist. And they are not to be confused with a tabletop PC. And they are mostly discontinued, though Lenovo still makes them.
https://www.amazon.com/Acer-Multi-Touch-Portable-Desktop-Computer/dp/B078SNDV6Q
https://www.intel.com/content/www/u...ones/what-is-a-portable-all-in-one-video.html
https://www.bestbuy.com/site/hp-env...1tb-hard-drive-silver/9008261.p?skuId=9008261