Precise calculations of core properties in heavy-atom systems that are described by the operators heavily concentrated in atomic cores, such as hyperfine structure and P,T-parity nonconservation effects, require accounting for relativistic effects. Unfortunately, four-component calculation of molecules containing heavy elements is very consuming already at the stages of calculation and transformation of two-electron integrals with a basis set of four-component spinors. In turn, the relativistic effective core potential (RECP) calculations of valence (spectroscopic, chemical, etc.) properties of molecules are very popular, because the RECP method allows one to treat quite satisfactorily the correlation and relativistic effects for the valence electrons of a molecule and to reduce significantly the computational efforts. The valence molecular spinors are usually smoothed in atomic cores, and, as a result, direct calculation of electronic densities near heavy nuclei is impossible. In this paper, the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component RECP calculation of a molecule are discussed. Their efficiency is illustrated in correlation calculations of hyperfine structure and parity nonconservation effects in heavy-atom molecules YbF, BaF, TIF, and PbO.