The Kopuster Hasidic dynasty was based on the Chabad school of thought.
The first three Rebbes of Chabad were Shneur Zalman of Liadi, Dovber Schneuri, and Menachem Mendel Schneersohn, also known as the "Tzemach Tzedek". When the Tzemach Tzedek died, he did not leave a clear successor. His son, Shmuel Schneersohn became the Rebbe in the city of Lyubavichi, known commonly as Lubavitch. Another son, Rabbi Yehuda Leib Schneersohn (the MaHarI"L, acronym for "Moreinu HaRav Yehuda Leib") became the Kopuster Rebbe (i.e., the Rebbe of Kopust or Kopes - accent on first syllable - known as Kopys in Belarus). However, he died soon after becoming Rebbe; his son Rabbi Shlomo Zalman took over the Kopuster dynasty thereafter. Rabbi Shlomo Zalman authored Magen Avos, a sefer on Hasidism.
The Tzemach Tzedek also left a number of other sons who became Rebbes respectively in the cities of Lyady, Babruysk, and Nizhyn.
There is reason to believe that during his short-lived reign, the MaHarIL actually had more followers than the then Lubavitcher Rebbe, Rabbi Shmuel. However, after his passing, many Kopuster Chassidim returned to Lubavitch. Even so, evidence suggests that Kopust remained as large or larger than Lubavitch even into the leadership of the Rebbe RaSHaB, the fifth Lubavitcher Rebbe.
There was very little antagonism between the branches of the Chabad hasidic movement - indeed the second and third rebbes of Kopes were sent to study in Lubavitch with the grandfathers and uncles.[1] Rabbi Menachem Mendel Schneerson, the last Lubavitcher Rebbe referred to the Rebbes of Kopes as "Admorim", (the acronym for Adoneinu Moreinu v'Rabeinu, a term for a Chassidic Rebbe or Grand Rabbi), indicating his respect for the Kopes dynasty.[2]
Yehuda Leib's oldest son Shlomo Zalman became the second Kopuster Rebbe on his death in 1866, on the latter's death in 1900 the Hasidim became followers of his brother, Shmaryahu Noah Schneersohn of Kopys, who was then the Rebbe of Babruysk. When the third Rebbe died in 1926 the Kopys Hasidim rejoined the then mainstream branch of Chabad hasidism, that of Lubavitch.[1]