An leading section of the previous party leadership did use the structure of the party to try and impose its own way. This went up to an international level with involvement of all sections. Because of the nature of the organisation - the culture within the organisaton as much as the democratic structures available - the result of this spat was the leaving of Ted Grant, Allan Woods and a section of the old leadership.
This was the major dispute at the end of the poll tax. Unfortunately 2 years of tearing ourselves apart resulted in losing all of the gains - the many people interested in the then Militant - that were a result of the poll tax campaign. Most folk who were vaguely interested thought (fully understandably...) feck that - this lot are as nuts as we have been warned they were
I would say more folk simply dropped out of activity than joined either faction.