From late 18th century into the Interwar Period Hluboká (Hungarian name Melyut) > Ungvar jaras > Ungvar megve/county > Karpatajla > Kingdom of Hungary > Austro-Hungarian Empire. In the Interwar Period it was part of Subcarpathia > Czechoslovakia. Post WW2 it became a part of SSR Ukraine.
Today selo/village Hlyboke (??????? in Ukr) is located near the Solotvynka River (coordinates 48.33-22.25 on Rte M17) and is clustered with selo Ruski Komarivtsi > Uzhorodskij raion/district > Zakarpatska oblast/region > Ukraine, latest zip 89430. Population 577.
During the Austro-Hungarian Period w/population of 483, the hamlet was predominantly German, Rusyn and Slovak.The filial Greek Catholic Church was in Nagylaz (Velyki Lazy) and both the filial Jewish Kahal and the filial Roman Catholic Church were in Szerednye (Serednye).
Neither surnames Babyak (????? in Ukr) nor Paduch (closest to English transliteration I could find might be ???????) appear in the village telephone directory.Since many villagers have migrated to the larger towns and cities, I found appx a dozen Babyak currently living in the regional capital, Uzhorod.There was one ?????? listed in Velyki Lazy White Pages.
Although this district has been filmed by LDS,unfortunately it is not indexed.You can make an inquiry at the Zakarpatska State Archives in Uzhorod.Cost may run appx $150USD.