The relativistic hadron cell model based on the conception of local equilibrium in the framework of the Planck formalism of the relativistic statistical mechanics was introduced. It was applied to describe the experimental data on the transverse momentum distribution of hadrons created in the heavy-ion and proton-proton collisions at high energies. In this model the topological forms of the spatial fireball and the speed field of cells are given by definition. In the case of the spherical spatial fireball, the speed of cells is given by two scenarios: the speed sphere with the spherical Hubble expansion and the speed spheroid with the longitudinal Hubble expansion and transversal radial explosion. In the case of the spheroidal spatial fireball, the speed of cells is defined only by the spheroidal Hubble expansion.