In view of his family relationship with Oda, Conrad the Elder was frequently referred to as nepos (nephew, grandson, descendant) of the Emperor.
He and his brothers apparently were in fact Arnulf's closest relatives, and he relied heavily on their support in his feud with the counts of Babenberg.
Arnulf rewarded them by helping them gain territories, beyond their original realm in Hesse, in Thuringia and the Frankish regions along the Main river.
After Arnulf's death, the Conradines were the only blood relatives of the new king, Louis the Child, and thus the dominant family in the kingdom.
Having largely failed to secure unity and order in the Empire in the face of obstinate resistance from the dukes of Swabia, Bavaria and Lorraine, Conrad, on his deathbed in December 918, persuaded his brother Eberhard, margrave and subsequently duke of Franconia, to forgo any aspiration for the crown for himself and to recommend to the Frankish nobles the election of the powerful duke of Saxony, Henry the Fowler (Henry I), as next king in order to ensure unity among the German tribes and preserve the Empire.