These assignments enabled him to ascend socially. It is plausible that he (or his unidentified ancestor) was granted the ancient estates of the kindred – including the eponymous village Pok (or Puk), which laid near Győr in Western Hungary. Mórichida (lit. "Maurice's Bridge") in the same region was named after him, where he erected a bridge over the river Rába. He had a namesake son Maurice II, who had become an influential advisor of King Béla IV of Hungary after the 1241 Mongol invasion and his kinship rapidly elevated into the one of the most powerful families in Hungary. The clan's Mórichida branch and its cadet branch, the Meggyesi family ascended from him. Maurice I's grandson was the influential provincial lord Nicholas Pok, who acquired large-scale domains in Northern Transylvania and Carpathian Ruthenia at the turn of the 13th and 14th centuries. Maurice I also had two another sons, John – a courtier of Béla, Duke of Slavonia – and Ded. Whether Amadeus Pok, Bishop of Győr or Thomas Pok, Master of the doorkeepers were also the children of Maurice I, is unknown.