I have some additional information about my KARNERs since my previous post. My great grandmother was Veronika KARNER, born in Bakonybánk in 1872. She was married to György MIKOLICS.
Veronika's parents were Márton Ferenc KÁRNER b. 1837 Bakonybánk and Mária NAGY b. 1841.
Márton KÁRNER's parents were Márton KÁRNER and Ágnes CSONKA. According to information from National Archives of Hungary, Márton and Ágnes had 11 children (I have the names). All but the eldest child were born in Bánk/Bakonybánk. I had received information previously that one of the children Ignatius (Ignác), b. 1831 Bánk and d. Csatka 1906, was married to Anna SARUS.
I am interesting in hearing from anyone with information or connection to this line of my ancestry.