The structure of a brush made of arm-grafted polymer stars is investigated using the Scheutjens-Fleer self-consistent field method. By using the "probe macromolecule" approach, conditional distributions of end- and branching points were obtained, which allowed for a detailed analysis of intramolecular correlations in the brush. Results strongly support a previously suggested "two population" picture of the star structure: stars in the brush are divided into two populations (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended toward the solvent. The stars in the "stretched" population have no arms that fold back toward the grafting surface and their free arms form a new sub-brush with effective grafting density determined solely by the total surface loading: molecular mass of polymer grafted onto unit area. With increasing grafting density or/and number of star arms the fraction of stars in the "stretched" population grows. The degree of backfolding of arms is estimated, the total fraction of backfolded arms is invariably small and decreases with increasing grafting density; only stars of the weakly extended population contribute to backfolding. The free ends within a given star are correlated: the ends of different arms are located approximately at the same distance from the grafting plane. Comparison of conditional ends distributions at fixed position of the branching points at different grafting densities reveals a conformational universality of grafted stars belonging to the weakly stretched population: the shape of the ends distribution does not depend on the grafting density but is determined solely by the position of the branching point. We also present analytical arguments showing that this effect is due to universal parabolic self-consistent potential acting on monomer units in the star brush, this potential is independent of the grafting density and the number of star arms.