How to move your capital

From Crusaderkings

Your realm's capital is determined when you load your game and periodically afterwards.

The capital move to the demesne province which

1. Has the same religion as your ruler
2. Has the same culture as your ruler
3. Has the highest (current?) income of the demesne provinces

To move your capital, you can

1. Give away provinces to your vassals
2. Convert rich heathen provinces by event
3. Convert rich non-culture provinces by event
4. Edit the provinces in your saved game