We summarize our findings on the quantum moduli constraints and superpotentials of an infinite family of moose extensions of $n_f = n_c$ SUSY QCD. For $n_c=2$, we perform concrete calculations using traditional integrating out techniques as well as Intriligator's ``integrating in'' technique. Checking the constraints and superpotentials in the limits of setting $Λ$'s to zero or integrating out mass terms, we find that the quantum moduli constraints are local in theory space and are equivalent to a consistent structure of ``splitting relations'' amongst the different theories. Extending the results to arbitrary $n_c$, we show that the splitting relations, along with a set of rules for flowing from a high energy theory to a low energy theory, incorporate much of the physics of the moose chain. The relations can be used both to simplify perturbative calculations of symmetry breaking and to incorporate nonperturbative effects.

25 pages, Latex; changed analysis on power-law running section now with weaker results, added references and acknowledgements