Michael Batanin, Monoidal globular categories as a natural environment for the theory of weak -categories , Advances in Mathematics 136 (1998), no. 1, 39–103.
Ross Street, The role of Michael Batanin’s monoidal globular categories, in Higher Category Theory, eds. E. Getzler and M. Kapranov, Contemp. Math. 230, American Mathematial Society, Providence, Rhode Island, 1998, pp. 99–116. (pdf)
A discussion of weak -functors between Batanin -categories, and all kind of weak -transformations in the spirit of Batanin approach, with an emphasis to the possibility to the existence of the weak -category of the weak -categories in Batanin’s sense is in
Camell Kachour, Steps toward the Weak -category of the Weak -categories in the globular setting, Published in Categories and General Algebraic Structures with Applications (2015).