karlin

Not quite. The Pinsk one is a break away faction of Karlin Stolin.

In short there was a break away (mostly) when the previous Stolin Rebbe zt”l was niftar and many of the Jerusalemite Karliners (mostly elders) saw no future Manhig within the Chassidus. So they turned to the Tzaddikim of Lelov, who were very close to them. The others (mostly younger generation) and those in America, waited on and accepted the leadership of the current Rebbe Shlita, who was young at the time. Needless to say this created a bit disharmony. This “arrangement” continued many years, until on fine day the Lelover Rebbe (forgot which one) decided enough is enough, and ended his leadership of the Karlin segment. Those stranded without a Rebbe chose for themselves Rabbi Aharon Rosenfeld as their Manhig. Originally they called themselves “Karlin”, after a ruling of Bais Din they distinguished themselves with the title Pinsk – Karlin.

In the Alter Heim A Rebbe could be the Rebbe of a town, but not really the next town because of the time to travel, so many times the sons would divide the followers that way

Not to pick on Satmar, but Kiryat Joel vs Williamsburg is a good example, they were too far away in the Alter Heim so the brothers would have just split it up and getan, but today travel between the 2 is pretty easy.

You now have the the Same Rebbe in many groups the same Rebbe in the US, Antwerp and Israel, that never would have happend as it was almost impossible for such travel

DaMoshe: Who says they can’t choose? As seen in many large kehillos such as Satmar, Bobov, Viznitz, Lelov etc. they have chosen.
Oyoy: 13th ave??