In what way do kinetochore microtubules facilitate the process of splitting the centromeres?

They produce tension by moving towards opposite poles.

Explanation:

In eukaryotes, the duplicated chromatids are attached with a disc shape protein called kinetochore. The assembly kinetochore occurs over centromeres. The centromeres joins two sister chromatids. The kinetochore connects the microtubules to the spindle at the time of meiosis or mitosis.

This allows separation of sister chromatids at the time of cell division. This results in two daughter cells. Thus, kinetochore produce tension by moving towards opposite poles.