  We consider the simplest representative of the class of multiply branched
polymer macromolecules, known as a pom-pom structure. The molecule consists of
a backbone linear chain terminated by two branching points with functionalities
(numbers of side chains) of $f_1$ and $f_2$, respectively. In a symmetrical
case, considered in the present study, one has $f_1=f_2=f$ with the total
number of chains $F=2f+1$. Whereas rheological behaviour of melts of pom-pom
molecules are intensively studied so far, we turn our attention towards
conformational properties of such polymers in a regime of dilute solution. The
universality concept, originated in the critical phenomena and in scaling
properties of polymers, is used in this study. To be able to compare the
outcome of the direct polymer renormalization approach with that obtained via
dissipative particle dynamics simulations, we concentrated on the universal
ratios of the shape characteristics. In this way the differences in the energy
and length scales are eliminated and the universal ratios depend only on space
dimension, solvent quality and a type of molecular branching. Such universal
ratios were evaluated both for a whole molecule and for its individual
branches. For some shape properties, theory and simulations are in excellent
agreement, for other we found the interval of $F$ where both agree reasonably
well. Combination of theoretical and simulation approaches provide thorough
quantitative description of the peculiarities of swelling effects and spatial
extension of pom-pom molecules and are compared with the known results for
simpler molecular topologies.
