[1] The kindred possessed lands in Central Transdanubia, primarily in Tolna and Komárom counties, centered around the namesake estate Szák.
[1] Conrad is first mentioned by a royal charter of King Béla IV of Hungary in May 1240, when he already served as Cup-bearer of the Queen's Court.
As a result, the king donated the village of Podár in Veszprém County (today a wasteland near Dáka) to Conrad.
Béla IV granted three of his former estates – Terjén, Gyalán and Várong – to Conrad in April 1250,[4] with the consent of Queen Maria.
[8] His relative, Pousa Szák bequeathed his estate in Bere (laid in present-day Márkó) in Veszprém County to Conrad in 1269.