In Crusader King’s III you may see next to your territory someone else’s territory fading into your color. This is known as the De Jure Drift and I will explain everything that is involved with it and how to speed up its process.
The De Jure Drift
When you are going to war in CK3 and you conquer a duchy that is part of a kingdom, slowly over the process of 100 years will pieces close to the conquered duchy of that kingdom begin to incorporate themselves into your kingdom and become yours de jure.
For example, in the picture below my Kingdom of Akan owns a duchy in the Kingdom of Gur which begins de jure drift process (100 years) of essentially consuming other duchies into being mine.
How to Speed Up the Process
Like using a head of faith to fabricate a claim, you use your chancellor to “Integrate Title” to make assimilation go faster. That being said, the drift may not be complete in the present Ruler’s lifetime still.
Problems That Can Occur and How to Fix Them
If the duchy that is drifting has decided to rebel against its liege, then the time for full incorporation into your realm will stop and begin to count backward instead of forwards. This can also happen if another independent realm wages war against it.
The only way I have found to fix a rebellion is to use intrigue and kill the leader because if they’re already leading a rebellion, it’s hard to appease them otherwise. If another independent realm has waged war on the duchy you could wage war on the independent realm and win and then have even more land.
As you can do this to other kingdoms, they can do it to you as well and begin a drifting process and take your kingdom. If this is the case, you can wage war against them and take back your piece of your kingdom to stop the drift.