  A notion of open rank, related with generic power sum decompositions of
forms, has recently been introduced in the literature. The main result here is
that the maximum open rank for plane quartics is eight. In particular, this
gives the first example of $n,d$, such that the maximum open rank for degree
$d$ forms that essentially depend on $n$ variables is strictly greater than the
maximum rank. On one hand, the result allows to improve the previously known
bounds on open rank, but on the other hand indicates that such bounds are
likely quite relaxed. Nevertheless, some of the preparatory results are of
independent interest, and still may provide useful information in connection
with the problem of finding the maximum rank for the set of all forms of given
degree and number of variables. For instance, we get that every ternary forms
of degree $d\ge 3$ can be annihilated by the product of $d-1$ pairwise
independent linear forms.
