We analyze the transverse momentum (pT) spectra of π+, π−, K+, K−, p, p¯, Λ, Λ¯, Ξ, Ξ¯, Ω−, Ω¯+ or Ω−+Ω¯+ in different centrality intervals in gold–gold (Au–Au) and lead–lead (Pb–Pb) symmetric collisions at 200 GeV and 2.76 TeV, respectively, by Tsallis–Pareto-type function. Proton–proton collisions at the same centre of mass energies are also analyzed for these particles to compare the results obtained from these systems. The present work extracts the effective temperature T, non-extensivity parameter (q), the mean transverse momentum spectra (⟨pT⟩), the multiplicity parameter (N0), kinetic freeze-out temperature (T0) and transverse flow velocity (βT). We reported a plateau structure of pT, T, T0, βT, pT and q in central collisions. Beyond the plateau region, the excitation function of all the above parameters decreases towards the periphery, except q, which has a reverse trend. The multiplicity parameter is also extracted, which is found to be decreasing towards the periphery from the central collisions. In addition, we observed that the excitation function of pp collisions is nearly the same to that of the most peripheral symmetric nucleus–nucleus collisions at the same colliding energy. Throughout the analyses, the same multiplicity parameters for particles and their antiparticles have been reported, which show the symmetric production of particles and their antiparticles.