According to a list of his possessions from 1285, he owned Bán, Régen, Alsásony, Szerk, Gesztence, Szentiván, Szombathely-Fertőfő, Göncöl, Rosenfeld and Csedefölde.
Through purchases and exchanges, he attempted to create a coherent and extensive lordship in Moson County, especially in the western and eastern parts, like his contemporaries throughout Hungary.
[1] Initially, he belonged to the courtiers of King Béla IV; he appeared as Master of the stewards in the court of queen consort Maria Laskarina in 1253.
[8] In the year 1258, Conrad filed a lawsuit against his second cousins, the wives of Paul Geregye and Stephen Csák, disputing the legitimacy of their ownership over Ilsva and Rahóca in Baranya County, respectively.
Béla IV rejected Conrad's accusations citing the two lady were granted the aforementioned possessions via daughters' quarter approximately thirty years ago.
Thus it is plausible he served in this capacity sometime in the period between 1254 (when the last known office-holder Baldwin Rátót is mentioned) and 1260 (when Conrad fall out of favor in the Hungarian royal court until he obtained pardon from Béla in the diploma).
[11] However, soon, Conrad turned against Béla IV, according to the above-mentioned royal charter issued in 1263, which suggests he defected to Ottokar II of Bohemia, after his army vanquished the Hungarian troops in the Battle of Kressenbrunn on 12 June 1260.
The document narrates Conrad invited and garrisoned Ottokar's Styrian soldiers in his fort at Óvár, and made plundering raids against the nearby villages and estates in Moson County.
At the same time, Ottokar issued a safe conduct to Conrad's lands at the border in order to avoid plunder and destruction during the war between the kingdoms.
[10] The king returned the estate Fertőfő-Szombathely to Conrad in 1267, while the Lébény monastery regained the villages Régen and Sásony (present-day Winden am See, Austria) in the same time.
Before 1270, Béla IV has authorized him the collection of duties at the bridge, where the Leitha flowed into the Moson arm of the Danube west of Szigetköz near his fortress.
Under such circumstances, Conrad had numerous conflicts and lawsuits with his neighbors and opponents, for instance the nobles of Kiliti (1274), Paul Gutkeled (1276), Peter Tétény and his family (1278–1279) and his toughest local enemy Herbord Hahót (1279), who looted and plundered his landholdings.
However the Győr kindred was embroiled in conflict with the influential local families, the Matucsinais (Kemény, son of Lawrence) and the Kórógyis, who plundered and seized their several lands in Baranya County in 1296, including Kéménd, Gyula, Olasz and Palkonya.
Conrad and his son James were granted exemption from the jurisdiction of the ispán by Andrew III of Hungary, but in reality this did not prevail due to the anarchic conditions.