The preservation of chain end functionality (CEF) is perhaps the most important criterion of the livingness for any controlled/living radical polymerization (CRP) system. CEF depends on several parameters but most importantly on concentration of propagating radicals, i.e., rate of polymerization. There are claims in the literature about ultrafast CRP leading to ultrahigh molecular weight with perfectly preserved CEF. However, faster CRP always results in lower CEF. Thus, how fast can a CRP be conducted with preserved CEF? In this paper we evaluate, by kinetic analysis and computation, the dependence of CEF on the rate of polymerization monomer structure (rate constants of propagation and termination), targeted degree of polymerization, initial monomer concentration, and monomer conversion. Some subtle differences in the definition of CEF are discussed for different types of atom transfer radical polymerization (ATRP) techniques. CEF for polymer chains with and without an alpha-alkyl group from a (macro)initiator are compared for a normal ATRP and initiators for continuous activator regeneration (ICAR) ATRP. The latter system closely resembles reversible addition-fragmentaion transfer (RAFT) polymerization.