Their last holding became known as the Emirate of Córdoba. It was not until the rule of the grandson of the founder of this new emirate that the state entered a new phase as the Caliphate of Córdoba.
The last territory they controlled was called the Emirate of Córdoba.  It wasn't until the grandson of the ruler who established this new emirate that the state transitioned into a new era as the Caliphate of Córdoba.