  Experimental data on inclusive cross sections of the hadrons produced in high
energy proton-(anti)proton collisions are analyzed in the z-scaling approach.
Saturation of the scaling function PSI(z) for z<0.1 (low transverse momenta)
was found. The first results on charged hadron spectra in pp collisions
obtained by the CMS Collaboration at the LHC have confirmed the saturation down
to the value of z=0.05. The CMS data on neutral K-meson production at s^{1/2}=7
TeV extend the saturation region even to a lower value of z=0.002 in the new
energy domain. A microscopic scenario of hadron production at a constituent
level based on the z-scaling is discussed in the saturation regime.
