High-performance cross-linked polymeric materials are now prepared from preformed precursors typical by distributions of molecular weights, number and reactivities of functional groups, and specific architectures. This makes theoretical treatment of networks evolution and their final structure difficult. This paper describes kinetically controlled cross-linking of a precursor formed from polyfunctional cores by arm extension by which molecular weight distribution develops and new groups of different reactivity are formed. These precursors are then cross linked with a polyfunctional cross-linker. If the precursor groups react independently, a random (binomial) distribution of reactive groups results and the gel point conversion and other network parameters are independent of the differences in reactivity the groups with the cross linker If the condition of random (binomial) distribution is not met (fixed numbers of groups or substitution effect in the precursor molecules), this independence does not exist Relations for molecular weight averages prior to gelation and gel fraction and concentration of elastically active network chains in the postgel state are derived. This general treatment applies to precursors obtained by a wide variety of chain extension chemistries and any of the family of cross linking reactions of A + B type. In the second part, the general form of the theory was adapted to describe polyether precursors prepared by addition of an epoxy ester (glycidyl pivalate) to multifunctional polyols and their curing with a tri-isocyanate. Some of the primary OH groups of the core are chain extended to form a polyether chain terminated by a secondary OH group. The distributions are altered by additional reactions - transesterification and alcoholysis. The branching theory was modified and the results compared with experiments. Gel point conversions were affected by these additional reactions, but the concentration of elastically active network chains (EANCs) (calculated from equilibrium elastic modulus) did not change much. The fraction of formed bonds wasted in cycles amounted to 12-22%.