Universality of gelation: End-linking versus cross-linking and stiff rods versus flexible chains

End-linking is the process in which junctions that permanently connectl ends of polymers are introduced at random. Sufficient end-linking causes a system of polymers to undergo a continuous equilibrium phase transition from a liquid to an amorphous solid state, i.e., to gel. This gelation transition is explored for a variety of end-linked polymer systems, focusing on universal aspects, and is contrasted with that caused by cross-linking. The dependency of this phase transition on the single-chain statistics and on the functionality lof the junctions is investigated. As an example of a single-chain statistics, stiff rods with a finite bending energy are considered. The shear modulus and the distribution of localization lengths are calculated, and found to be universal near the transition.