A similar entry appears in the Wheel of Time Companion confirming the information available in the main story arc.
The Erinin is one of the longest rivers in the main continent, originating in the Spine of the World close to the Niamh passes and running west along the southern border of Shienar and Arafel before turning south (Reference: Map). It splits near to Dragonmount, with the island of Tar Valon in the center. The northern branch, the Esendrelle Erinin has the villages Luagde, Daghain and Osenrein and the southern branch, the Alindrelle Erinin, with the villages of Jualdhe, Darein and Alindaer. Each village has a bridge crossing to the city (TWoRJTWoT, Ch. 24).
It continues south along the Cairhienin border and then the border between Cairhein and Andor before passing between Aringill and Maerone on opposite banks, eventually heading to Tear and ending in the Delta known as the Fingers of the Dragon. South of Maerone, there are very few villages along the banks (LoC, Ch. 6). Other towns include Jurene (TDR, Ch. 39).
Tributaries include the Mora, which runs along the border between Arafel and Shienar and joins the Erinin at the southern border, the Alguenya which passes through Cairhien and joins the Erinin at Aringill and the Luan, which joins west of Caralain Grass and north of Braem Wood.
In earlier times, it marked the border between southern border of Rhamdashar with Hamarea, Ileande and Tar Valon, Shandalle and Caembarin, Khodomar and Esandara and between Fergansea and Moreina. During the time of the Ten Nations, it separated Coremanda and Almoren, though it is not clear if it was the border, or if the border merely followed it (Reference: The World of Robert Jordan's "The Wheel of Time").