Our main goal is to provide comparative analysis of several procedures for endogenous dynamic formation of the cooperation structure for TU games with major player [5, 6]. In the paper we consider both approaches to endogenous graph formation, of Aumann and Myerson [1], and of Petrosyan and Sedakov [7]. For the evaluation of the pros and cons when adding of a new link is in question, along with the Myerson value [4] we consider also the average tree solution introduced by Herings, van der Laan, Talman and Yang in [2] and the centrality rewarding Shapley and Myerson values, recently introduced by Khmelnitskaya, van der Laan and Talman in [3].