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The outer automorphism group $\text{Out}(\Gamma;\mathscr A)$ of a group$\Gamma$ relative to a free factor system $\mathscr A$ of $\Gamma$ acts byisometries on the relative free splitting complex $\mathcal{FS}(\Gamma;\mathscrA)$, which is Gromov hyperbolic. This is the first of a multipart study ofstable translation lengths of elements of this action, a quantitativegeneralization of earlier work on $\text{Out}(F_n)$. In this first part westate and prove the Two Over All Theorem, expressing a uniform exponentialgrowth property along Stallings fold paths in $\mathcal{FS}(\Gamma;\mathscrA)$, and we give two applications of that theorem. First, the natural map fromthe outer space $\mathscr O(\Gamma;\mathscr A)$ to the free splitting complex$\mathcal{FS}(\Gamma;\mathscr A)$ is coarsely Lipschitz, with respect to thelog-Lipschitz semimetric on $\mathscr O(\Gamma;\mathscr A)$. Second, if $\phi\in \text{Out}(\Gamma;\mathscr A)$ has a filling attracting lamination withexpansion factor $\lambda>1$ then the stable translation length of $\phi$ on$\mathcal{FS}(\Gamma;\mathscr A)$ has an upper bounded of the form $B\log(\lambda)$.

Stable Translation Lengths on Free Splitting Complexes I: The Two Over All Theorem and its Applications