  We prove Vojta's generalized abc conjecture for algebraic tori over function
fields with exceptional sets that can be determined effectively. Additionally,
we establish a version of the conjecture for toric varieties. As an
application, we investigate the Lang-Vojta Conjecture for varieties of log
general type that are ramified covers of $\mathbb G_m^n$ over function fields.
In particular, we consider the case of $ \mathbb P^n\setminus D$, where $D$ is
an algebraic curve over a function field in $\mathbb P^n$ with $n+1$
irreducible components and $\deg D\ge n+2$. Our methods also apply to the
complex situation, enabling us to find explicit exceptional sets for the
corresponding case of Vojta's general abc conjecture (complex version) and the
Green-Griffith-Lang conjecture.
