It depends on what kind of AAR I plan on writing. When I know I’m going to write a narrative then I don’t take any notes at all. Since my narratives are usually very light on gameplay, notes haven’t been that important to me.
If you choose to write up a comedy, some notes are important but you could get by with just screenshots if you’re lazy.

Before Vik II for my B3 AARs I took notes but they were never as heavy as my pure gameplay AARs. In these I write about battles that are important, surprises, weird stuff, etc. Winging it is fairy easy.
As far as notes go, Gameplay and History Book always has the same amount of heavy notes with me. I write down everything except for what pics say. This will make it so I don’t have to write everything down. Also I abbreviate almost everything in my notes. Going back to Victoria II again, NF = National Focus; MA = Military Access; Ally = Alliance or Allied; DoW = Declaration of War; Port = Portugal; etc. And whenever I take a picture I place an asterisk next to the month and day. Below is a random page for my next history book - anything in bold is my explanation here and wasn’t written down on the paper:
*May 24, mind of westernization
I took a pic of this so I wouldn’t have to bother writing down the province. I take pics also if there is more than one choice available and I can see the positives and negatives of the decision.
June 17, deny MA to Egypt
I only mentioned this in my notes because at the time Egypt and the Ottomans were at war
July 1, election over
Con 43.87%
Hash 28.06%
Lib 28.06%
At this point I only had three parties so abbreviations are still simple. Con = conservative; lib = liberal; hash = Hashemite
Con wins
Aug 14 Greece in OE SOI
Sept 8 debt repaid. All taxes back to norm except rich @ 49%
Oct 10 poor and mid tax 39%
“ 21, Aristocrats in Kuwait angered over reform
Nov 5, begin construction of 4 MOW; all taxes 49%
* Dec 19, pic
I don't know what this pic is until I sit down to write the update. Or if I look ahead.
1850
Con 41.28
Reac 20.33
Lib 38.38
The above comes from my keeping an eye on the movement of the upper house
Feb 1, Afghanistan DoW Panjab
March 28, Arabian Army gen dies
May 10, mid tax 32% nat stock 8%
“ 11, Port DoW Zulu
Aug 14, nat stock 5%
Sept 29, US & OE wp
Oct 8, mid taxes 39%
Nov 18, Japan in US SOI
And all the above is one handwritten page. The way I see it is this: If I need to, I can always skip over extra information. Its easier to remember if its written down and you might not remember if it isn’t. It comes down to how detailed you want to be.
If you're going to do something in CK II, what you could try is a mini AAR of 5 - 10 years, wrap something up and that will give you an idea of how many notes you’d ideally like to take for a full AAR.
Edit: And yes, everything is on paper. I've had some trouble with computers and my AARs in the past so I try not to leave anything stored on it too long.