The ferrimagnetic spinel oxide Zn(x)Fe(3-x)O(4) combines high Curie temperature and spin polarization with tunable electrical and magnetic properties, making it a promising functional material for spintronic devices. We have grown epitaxial thin films with 0<=x<=0.9 on MgO(001) substrates with excellent structural properties both in pure Ar atmosphere and an Ar/O2 mixture by laser molecular beam epitaxy. We find that the electrical conductivity and the saturation magnetization can be tuned over a wide range during growth. Our extensive characterization of the films provides a clear picture of the underlying physics of this spinel ferrimagnet with antiparallel Fe moments on the A and B sublattice: (i) Zn substitution removes both Fe3+ moments from the A sublattice and itinerant charge carriers from the B sublattice, (ii) growth in finite oxygen partial pressure generates Fe vacancies on the B sublattice also removing itinerant charge carriers, and (iii) application of both Zn substitution and excess oxygen results in a compensation effect as Zn substitution partially removes the Fe vacancies. A decrease (increase) of charge carrier density results in a weakening (strengthening) of double exchange and thereby a decrease (increase) of conductivity and the saturation magnetization. This scenario is confirmed by the observation that the saturation magnetization scales with the longitudinal conductivity. The combination of tailored films with semiconductor materials such as ZnO in multi-functional heterostructures seems to be particularly appealing.