Unconstrained BRST superfield theories

We re-examine the use of a superspace to geometrically formulate BRST and anti-BRST symmetries in ordinary and supersymmetric field theories. We show that the conditions that curvature components should be trivial in the BRST superspace directions always result in differential equations whose solutions lead to prepotentials. We give the explicit solutions to many of these cases and show that the prepotentials play a crucial role in writing all actions in a manifestly invariant and geometrical form. (orig.)