Advances in synthetic polymer chemistry and nanotechnology applications of polymers lead to the necessity of designing complex architectures in order to combine the observed properties of more simple structures. Such complex architectured polymeric materials are the dendritic polymers exhibiting unique potentials, reasons that made them useful in many potential applications ranging from biochemistry to microelectronics. A dendritic structure is considered as an architecture including random hyperbranched, dendrigrafts and dendrimers. The interest of the theoretical studies is mainly concentrated on three of their properties useful for daily applications. First, the dendritic macromolecules have a high surface and numerous terminal ends. This leads to high density of the end groups leading to enhanced catalytic activity or high reactivity. The second useful property comes from the density fluctuations and cavities which are positive for the use of these materials as carriers of small molecules. This second property is often combined with their third property of the capability of an increased permeability to the interior of a macromolecule.

The conformational properties of dendritic homopolymers were studied via analytical theory and Monte Carlo simulations using coarse graining models. The radii of gyration and the length of the branches of zeroth and first generations were calculated via off-lattice, lattice algorithms and renormalization group techniques. The theoretical findings were compared with the respective results of star polymers with the same functionality and equivalent branch lengths. Furthermore, a microscopic model was used to determine analytically the macroscopic conformational properties of dendritic polymers with interactive branching points. We described the dependence on the number g of generations, the molecular weight N of each branch, the functionalities f and fc of the branching points and the core as well as the quality of the solvent. A comparison is given between the analytical results and the results from Monte Carlo simulations up to g=4 and fc=f=3. Finally we have studied the conformation properties of dendritic structures with homopolymer and copolymer grafted chains using off lattice Monte Carlo simulations. Several shape measures were used for the characterization of the shape anisotropy, asphericity, and acylindricity for a variety of dendrimer generations, grafted polymeric chain molecular weights and solvent conditions of the aforementioned complex structure.