Abstract
We study the process $e^-e^+\to ZH$ where $H$ represents the standard model (SM) Higgs particle $H_{SM}$, or the MSSM ones $h^0$ and $H^0$. In each case, we compute the one-loop effects and establish very simple expressions, called supersimple (sim), for the helicity conserving (dominant) and the helicity violating (suppressed) amplitudes. Such expressions, are then used to construct various cross sections and asymmetries, involving polarized or unpolarized beams and Z-polarization measurements. We examine the adequacy of such expressions to distinguish SM or MSSM effects, from other types of BSM (beyond the standard model) contributions.