The independence of early Tosafist works notwithstanding, it is important to realize that talmudic scholars never operated in a complete intellectual vacuum. Indeed, most Tosafists approached the talmudic text with the analysis of the earlier generations as a backdrop for their own analysis. In addition to engaging in the independent dialectics that typified the earliest Tosafist period, subsequent Tosafists also had the challenge of relating to the Tosafists that preceded them.
For the independent early Tosafists the Talmud text itself was the focal point of study, as they focused on identifying contradictions, suggesting resolutions, analyzing relevant passages, and other forms of commentary. However, in the following generations attention was also directed toward the works of the early Tosafists. Contradictions had been identified by the early Tosafist masters, and oftentimes multiple resolutions had been suggested by the different early masters. A later Tosafist had to collect the relevant discussions and weigh the strengths of the suggested solutions. In turn this would lead the later Tosafist to ultimately choose which questions, comments, comparisons, and resolutions he wished to teach to his students and integrate into his own commentary.
Aryeh Leibowitz, “The Emergence and Development of Tosafot on the Talmud”, Hakirah 15 (Summer 2013), 153.