Monte Carlo simulations of a simple cubic lattice model of star-branched polymers were made. The solvent conditions (temperature) were varied in a wide range and the total chain length was up to 800 beads. The analysis of a shape of branched macromolecules was performed by means of the gyration tensor principal moments and asphericity factor. The changes of shape parameters during the transition from a random coil to a collapsed globule have been determined. In high temperatures, the instantaneous shape of the branched chain is more symmetric than that for linear chains. The shape of one star arm is very similar to that of the entire polymer. In lower temperatures, the collapsed model chain forms an isotropic globule. The shape of inner and outer parts of the star polymers is discussed.