This paper describes topological searches for neutral scalar bosons S-0 produced in association with a Z(0) boson via the Bjorken process e(+)e(-) --> S(0)Z(0) at centre-of-mass energies of 91 GeV and 183209 GeV. These searches are based on studies of the recoil mass spectrum of Z(0) --> e(+)e(-) and mu(+)mu(-) events and on a search for S(0)Z(0) with Z(0) --> v (v) over bar and So --> e(+)e(-) or photons. They cover the decays of the S-0 into an arbitrary combination of hadrons, leptons, photons and invisible particles as well as the possibility that it might be stable. No indication for a signal is found in the data and upper limits on the cross section of the Bjorken process are calculated. Cross-section limits are given in terms of a scale factor k with respect to the Standard Model cross section for the Higgs-strahlung process e(+)e(-) --> H(SM)(0)Z(0). These results can be interpreted in general scenarios independently of the decay modes of the S-0. The examples considered here are the production of a single new scalar particle with a decay width smaller than the detector mass resolution, and for the first time, two scenarios with continuous mass distributions, due to a single very broad state or several states close in mass.