The title of Count of Zutphen historically belonged to the ruler of the Dutch province of Gelderland (Zutphen being one of the major cities in the province during the medieval period).
The line of the Counts of Zutphen became extinct in the 12th century and the title passed onto the rulers of Burgundy then from then to the King of Spain until Gelderland became one of the provinces to revolt and form the United Provinces.
The House of Zutphen comes into existence in 1018 when Otto of Hammerstein becomes the first Lord of Zutphen. In 1046 Henry III, emperor of Germany gives Zutphen to Bishop Bernold of Utrecht. The Lords of Zutphen do not recognize this gift, which leads to some confusion regarding who actually owns Zutphen.
After Ludolf's death it is possible that Zutphen was always intended for Adelheid of Zutphen. It would eventually go to her husband Gottschalk.