Recently, a method to compute the implicit equation of a parameterized hypersurface has been developed by the authors. We address here some questions related to this method : optimality of a degree estimate and determination of an extraneous factor that appears when the base points are not locally complete intersections. We then make a link with a resultant computation for the case of rational plane curves and for particular cases of space surfaces. As a consequence, we prove a conjecture of Busé, Cox and D'Andrea.