I do not know the exact answer, but I'm pretty sure you won't have a problem going from one desktop to another. I do not believe the information is stored as a cookie - it would be a miniscule file, and I'm sure those notes are stored on the server.
Btw, I copy my analysis and paste it directly to Notes. I don't bother to space it out, since it isn't that hard to read anyway.
Apparently one answer is 'at least 45k'. I seem to have saved that much in the text for the notes for one game. I should probably erase it because there could be a limit on the total text for an account too.
Duh! Here is how I managed to confuse myself. I may be somewhat spacy, but this is pretty easy to have happen if you have a lot of windows open or leaving it and coming back later ...
Go to an online game. Look at the Notes there. Open an analysis board. Edit the notes there, and save them. Close the analysis board. Look at the notes on the main page for the game. Oh no, where did my notes go?????
You just have to reload the main page, and they will be there. It took me awhile to figure that out, too.
Another way to handle it is to just copy the moves from analysis, and then close the analysis window and paste them in the main notes. Not necessary, but it's nice to actually see the notes working!
I've been using the Notes to write a lot of analysis. (This is unusual for me but I am especially motivated by one particular game.) I seem to notice they don't always store properly. Partly it is because I am on a PalmOS tablet sometimes, and the 'save note' button just doesn't work I think. But also I am wondering if I have a desktop and a laptop with Firefox and the javascript works OK, and I write a note on one of them to say xxx yyy, and then I go and edit it on another computer to say xxx yyy zzz, is there any chance the first computer would fail to pick up the change? This could happen if caching got in the way or if the note is stored in cookies. Also I would like to know the maximum possible length, since I am worried about possibly losing information if my analysis gets to be too long. I would be somewhat sad if I lost what I wrote! Thank you!