The conformational properties of Hybrid Dendritic Star copolymers (HDS) which combine the characteristics of dendrimers with those of flexible polymers are studied, for the first time, by means of Off Lattice Monte Carlo simulations. Using the efficient Pivot algorithm we calculate the asphericity and the acylindricity of the whole molecule for various solvent conditions and different characteristics of dendritic and star chains. Moreover, the effects of the number and the length of star branches on the conformation of the dendritic part are also studied. By considering the HDS copolymers as 'hairy spheres' we have calculated the star monomer distribution profiles. The shapes of the profiles are compared with previous Monte Carlo results. (C) 2008 Elsevier Ltd. All rights reserved.