His father was Maran HaGaon HaRav Yaakov Kantorovich zt”l, which those that knew him (including his nephew HaGaon HaRav Moishe Feinstein zt”l) held of him as the Gaon HaDor. He was Rav of Timkavitch in Russia and at the end of his life, when the communist took over Russia, and all rabbonim’s lives were in danger, he and R’ Moishe were of the last Rabbonim to escape to America where HaRav Kantorovich bacame rav of Trenton, NJ. He authored Tzilusa DeShmaatsa on the Shev Shmaatsa, Chidushei HaGR”Y and other seforim.

Rabbi Avroham Kantrowitz came from a strong lineage of gedolei hadoirois, as detailed in the biography of the new edition of his father’s sefer Chidushei HaGR”Y vol. I.
Rabbi Avroham Kantrowitz’s brother-in-law was HaGaon HaRav Yaakov Moishe Shurkin z”l.
Maran HaGaon HaRav Moishe Feinstein z”l was his first-cousin.
Maran HaGaon HaRav Michel Feinstein z”l, HaGaon HaRav Yoshe Ber Soleveitchik z”l and HaGaon HaRav Ahron Soloveitchik z”l were his first-cousins once-removed.