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Horizontal branch (HB) morphology is a complex multiple-parameter problem.Besides the metallicity, two other leading parameters are the mass loss rate(MLR) and the initial He abundance of the HB progenitors. Using the STAREVstellar evolution code, we produce a wide array of Extreme Horizontal Branch(EHB) stars and also examine their post-HB evolution. EHB stars are produced inour calculations by the so called `delayed (late) hot core flash' scenario. TheMLR is increased on the red giant branch (RGB) to the extent that, prior toreaching core flash conditions, only a very thin H-rich envelope remains andhelium ignition takes place at hotter positions on the HRD. We perform anextensive, self-consistent parameter study, covering populations I and II(Z=0.0001-0.03), for both normal initial helium abundances and He-enrichedmodels (up to Y=0.40). For completeness of the study and in order to point tocomplete trends, we chose NOT to cut out several combinations (or results of)that may extend beyond realistic limits. We present results and completeevolutionary tracks for the covered parameter space, showing in particularthat: a) Increased He abundance ON ITS OWN -- without having asignificant-enough MLR on the RGB -- DOES NOT lead to the production of EHBstars; however, b) The bluest (hottest) HB positions do result from theCOMBINED effect of He-enhancement and increased MLR; c) The general trend isthat the effective temperature on the HB increases with decreasing metallicity,but there is an indication for a halt, or even a reversal of this trend, as Zfurther decreases below $10^{-3}$; d) EHB stars can serve as major contributorsto the UV flux emanating from their host system. Thus, the presentcomprehensive study both complements and lends support to previous, morerestricted studies of the HB phase, and adds results for unexplored regions ofthe parameter space.

An Extensive Grid of Models Producing Extreme Horizontal Branch Stars