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Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamination, and (3) the sequence divides into a finite set of subsequences, each of which projectively converges to one of the ergodic measures on the ending lamination. The conditions are sufficiently robust, allowing us to construct sequences on a closed surface of genus  g  for which the space of measures has the maximal dimension3  ⁢  g   -  3{3g-3}   , for example.

Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II