The Three Families

In Apocrypha, the Three Families are the magi who constructed the Fuyuki Holy Grail War… in other words, the Einzberns, Tohsaka and Makiri.
Just as alluded in the light novels, Makiri (Matou) Zouken fought fiercely against Darnic during the Third Holy Grail War, but became practically crippled due to the shock of the Greater Grail being stolen. The family wasn't blessed with a successor either, so their future as magi has been completely shut.
The Tohsaka gave up on the Greater Grail, and now seek a new path in becoming one with the universe with Chinese Kenpou while learning magecraft. The twin-tail daughter of the family might also end up becoming the founder of a “completely new martial arts that combines magecraft and Chinse Kenpou” by the time she becomes a high school student. However, she never imagined that her younger sister who was adopted by distant relatives would come visit her in Japan after becoming a pro-wrestler with unimaginably nice proportions and forming a tag team with a drill-roll-haired girl…!
The Einzberns are in the midst of struggling to make a new Greater Grail under the excuse “It was stolen, so we'll just make a new Holy Grail.” Fortunately, in the Apocrypha world, a certain dead fish-eyed mercenary won't end up becoming involved with the Einzberns, so their greatest work Illyasviel will never be born—therefore, as long as she isn't born, the Einzberns will never despair… Is that really fortunate?

Fate/Apocrypha material: Fate/Apocrypha Encylopedia