  We show that any convergent (shuffle) arborified zeta value admits a series
representation. This justifies the introduction of a new generalisation to
rooted forests of multiple zeta values, and we study its algebraic properties.
As a consequence of the series representation, we derive elementary proofs of
some results of Bradley and Zhou for Mordell-Tornheim zeta values and give
explicit formulas. The series representation for shuffle arborified zeta values
also implies that they are conical zeta values. We characterise which conical
zeta values are arborified zeta values and evaluate them as sums of multiple
zeta values with rational coefficients.
