## 1 Introduction  
Silicon polymers, due to human friendliness and universal properties, constitute a wide group of various materials and have been used in many areas of everyday life. For instance, due to their excellent chemical, physical and electrical properties, they are widely used in the food and cosmetics industry [1, 2, 3], medicine [4, 5, 6], electronics [7, 8, 9, 10], building construction and as adhesion promoters [11, 12, 13]. The most common polymer of this kind is polydimethylsiloxane (PDMS), having a backbone consisting of siloxane groups (Si-O-Si) with two methyl groups on each silicon atom. Polysiloxanes are obtained in a three-step synthesis. The substrates are elemental Si (obtained by high temperature reduction in silicon dioxide (quartz or silica)) and methyl chloride. The products of direct Rochow's process are chlorosilanes [14, 15, 16, 17]. In the next step, they undergo hydrolysis to form linear or cyclic dimethylsiloxane oligomers, which in the final stage are subjected to, respectively, polycondensation or chain polymerization, catalyzed by acids or bases. Due to the lack of diversity in structure and properties, there is a great need to modify polysiloxanes by introducing various functional groups into their structure. An example of such a modification is the introduction of functional groups at the synthesis stage: azide groups (capable of 1,3-dipolar cycloaddition reactions), vinyl groups (giving many pathways of modification, including hydrosilylation or thiol-ene reaction) or amine groups (capable of Michael addition). Such activities are aimed at improving individual properties of materials and creating a range of materials for new applications [11; 18; 19; 20; 21]. Over the past decades, dendritic polymers, particularly dendrimers and hyperbranched polymers, have attracted extraordinary interest. This class of macromolecules exhibits unique, architecture-correlated properties. Among others, the properties include: unusually low dispersities of molar masses, Newtonian fluid characteristics even at very high molar mass, encapsulation abilities in host-guest interactions, as well as much smaller hydrodynamic volumes, much more compact molecules, much higher solubilities and much lower viscosities than their corresponding linear analogs of the same molar mass [22; 23]. Researchers have also focused on the synthesis of silicon-based hyperbranched polymers prepared with a relatively narrow set of reactions, such as hydrosilylation, Grignard reactions and controlled condensation of silanols. Complete conversion of all functional groups is necessary for creating well-defined dendrimer molecules; however, it might be a challenge due to a large number of functional groups at one macromolecule, which must undergo reaction at the same time (generation) [24]. The Piers-Rubinsztajn reaction for the preparation of siloxane, carbosilane and carbosiloxane hyperbranched structures is extensively utilized. Basically, monohydrotrisiloxanes (e.g., Heptamethyltrisiloxane) react with trialkoxyvinylsilanes; then, branched siloxanes and low molar mass alkanes are generated in the presence of BCF (B(C\({}_{6}\)F\({}_{5}\))\({}_{3}\)) as a catalyst [25; 26; 27; 28; 29; 30; 31; 32; 33], whereas in order to obtain carbosiloxanes, the other type of reaction has to be applied (Figure 1). It can include hydrosilylation process, for instance, which is based on the addition reaction between unsaturated bonds (e.g., CH=CH\({}_{2}\)) and silicon\(-\)hydrogen (Si\(-\)H) bonds in the presence of a platinum complex catalyst [34; 35; 36]. Another group are dendrimers, consisting of polyhedral oligomeric silsesquioxanes (POSS) as a core, obtained utilizing various techniques, depending on the groups introduced into POSS core. Recently, POSS molecules have attracted a lot of interest in chemistry. Their use as a core of a dendrimer has some advantages.