When did the Muslim rulers of Spain secede from the Arab Caliphate?

Abd ar-Rahman III was able to unite the divided lands of the Cordoba Caliphate and repulse the Fatimids. Thus, since 929, the Cordoba Caliphate existed as a completely independent state. Also, Abd al-Rahman III was able to push Christians further north with the help of military force and diplomacy. We can say that the 10th century for the Cordoba Caliphate was the period of the highest prosperity. However, in the 11th century, its decline begins. After the death of Hakam 2, strife breaks out in the Caliphate, which leads the Caliphate to disintegration.