My favorite source is Hugh Kennedy and he talks about the Taifas as follows:
1) Arab patrician taifas: Seville, Zaragoza and Cordoba
2) The old Berber taifas: Badajoz, Toledo, and Albarracin
3) The saqaliba taifas of the Levante
4) The Zirids of Granada and other 'new' Berber taifas
The taifas were followed by the alMoravids who we have not worked on. Then another period of taifas. Then the Almohad Caliphate. Then the Nasrids in Granada.