Actually, the same short-term memory and muscle memory that allow you to have an "output buffer" when typing works with hand writing. You can finish writing a word, maybe even a sentence, while thinking about something else.

If you look at the paper sheet, it is because you have to check you are still on the guideline.

However I believe that at uni, I would write a whole line without looking if I needed to (that's after about a decade of fast hand writing almost 8 hours a day, 4-5 days a week, though). That those lines had a tendency to go up or down was not a problem, because making a clean copy of those notes was part of my learning strategy.