Magnetic relaxation experiments at low temperatures were performed in different zero‐field‐cooled (ZFC) and field‐cooled (FC) high‐Tc superconductors (HTSCs): TlBaCaCuO (2212 and 2223 phases, polycrystalline and thin‐film samples), (Hg,Tl)BaCaCuO (1223 phase, polycrystalline material), and (Bi,Pb)SrCaCuO (2212 phase, single crystal). For each system and in the whole temperature range investigated, the relaxation curves obtained after both cooling processes are linear with the logarithm of time. The temperature dependence of the relaxation rate normalized to the first magnetization value, R=‖d(M/M0)/d ln(t)‖, follows a trend which is common to all systems: R decreases linearly with decreasing temperature down to a value, which is called the crossover temperature, below which it levels off to a T‐independent plateau. This behavior gives evidence of a transition in the mechanism responsible for the relaxation process at low temperatures, from thermally activated (linear dependence on T) to quantum vortex mot...