We consider random triangulations of a disk with k holes and N triangles as N → ∞. The coefficient λ ^m, λ > 0, is assigned to a triangulation with the total number of boundary edges equal to m. In the case of two boundaries, we separate three domains of variation of the parameter λ, and in each of them find the limit joint distribution of boundary lengths. For a greater number of boundaries, we give an algorithm to calculate the generating functions for the number of multi-rooted triangulations depending of the number of triangles and the lengths of boundaries. In Appendix, we discuss the relation between multi-rooted triangulations and unrooted triangulations, and give analogues of limit distributions for unrooted triangulations.