I actually do all this stuff in my head and use hierarchies of bullet points in a text file to externalize some stuff. Some of these may end in arrows that point to a different process.

I never use paper because I'm always moving these bullet points around and inserting stuff between them. Apps are too slow.

I never write down all the information because these notes are enough for me to reload everything. It's pretty easy to see that I didn't write something when there's a gap in my notes. I never wrote it down because I'm going to come up with the same or better solution quickly.

This isn't really helpful for anyone else and doesn't work well with pair programming.