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• The extension of the theoretical model describes spin-resolved electron transport in nanoscale magnetic contacts and heterojunctions. • Unified description without residual terms is shown for the point-like contact resistance from the Maxwell diffusive transport through the quasi-ballistic and ballistic to the purely quantum one. • The model shows a solution of the integro-differential equation for the electron transport which takes into account the second-order derivatives of the Green functions by z (coordinate along a transport direction). • The nonmagnetic approach of the theory matches the experimental data for golden nanocontacts. • A novel model is applied to describe domain wall resistance in magnetic nanowires. The work represents the extended theoretical model of the electrical conductance in nanoscale magnetic point-like contacts. The developed approach describes diffusive, quasi-ballistic, ballistic and quantum regimes of the spin-resolved conductance that is important for further development of the contact Andreev reflection spectroscopy, heterojunction models, scanning tunnel microscopy techniques. As a benefit, the model provides a unified description of the contact resistance from Maxwell diffusive through the ballistic to purely quantum transport regimes without residual terms. The model of the point contact assumes that the contact area can be replaced by a complicated object (i.e. the tunnel barrier or complicated one with nanoparticles, narrow domain wall, etc.), where the potential energy profile determines its electrical properties. The model can be easily adapted to particular contact materials, its physical properties and species of the contact area. [ABSTRACT FROM AUTHOR]