In a previous paper, the authors laid the foundations of a theory of Schatten–von Neumann classes [Gfr ]p (0<p[les ]∞) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant dˆ that relates the Hilbert–Schmidt norm of a form with its bounded norm behaves like n. Some results are also obtained in the quasi-Banach case (0<p<1), and for two-bounded forms. Finally, the domination problem is investigated in the trilinear set-up.