One common theme is growth. Baki is often on a journey of self - improvement in his fighting skills, and Kozue is there to support him. So, many fanfics show how their relationship evolves as Baki grows stronger.
One popular 'baki x kozue fanfic' is 'The Journey of Baki and Kozue'. It focuses on their relationship development in a more adventure - based setting, with Baki's strength and Kozue's supportiveness being key elements.