Horizontal branch ( HB ) morphology is a complex multiple-parameter problem . Besides the metallicity , two other leading parameters have been identified to be the mass loss rate ( MLR ) and the initial helium abundance of the HB progenitors . Using the STAREV stellar evolution code , we produce a wide array of Extreme Horizontal Branch ( EHB ) stars and also examine their post-HB evolution . EHB stars are produced in our calculations by the so called ‘ delayed ( late ) hot core flash ’ scenario . The MLR is increased on the red giant branch ( RGB ) to the extent that , prior to reaching core flash conditions , only a very thin hydrogen-rich envelope remains and helium ignition takes place at hotter positions on the Hertzsprung-Russell diagram ( HRD ) . We perform an extensive , self-consistent parameter study , covering populations I and II ( Z = 0.0001 - 0.03 ) , for both normal initial helium abundances and He-enriched models ( up to Y = 0.40 ) . For completeness of the study and in order to point to complete trends , we chose not to cut out several combinations ( or results of ) that may extend beyond realistic limits . We present results and complete evolutionary tracks for the covered parameter space , showing in particular that : a ) Increased He abundance on its own – without having a significant-enough MLR on the RGB – does not lead to the production of EHB stars ; however , b ) The bluest ( hottest ) HB positions do result from the combined effect of He-enhancement and increased MLR ; c ) The general trend is that 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 Z further decreases below 10 ^ { -3 } ; d ) EHB stars can serve as major contributors to the UV flux emanating from their host system . Thus , the present comprehensive study both complements and lends support to previous , more restricted studies of the HB phase , and adds results for unexplored regions of the parameter space .