We perform a representative series of semiclassical molecular dynamics simulations of aluminum nanocontact breakages, coupled to full quantum conductance calculations. This approach allows to obtain realistic conductance histograms of polyvalent species and understand the origin of their peaked structures. The results show that the conductance depends linearly on the contact minimum cross section for the geometrically favored nanocontact configurations. Valid in a broad range of conductance values, such relation suggests the definition of a transport parameter for the nanoscale, that represents the novel concept of ballistic resistivity. One of the major industrial challenges is to profit from some fascinating physical features present at the nanoscale. The production of dissipationless nanoswitches ͑or nanocontacts͒ is one of such attractive applications. 1 The inelastic electron mean free path is usually larger than nanocontact typical cross sections ͑of the order of few atoms in controlled experimets͒ even at room temperature, and, therefore, the electronic transport through these nanoconstrictions is expected to be ballistic. Nevertheless, the lack of knowledge of the real efficiency of this electronic ballistic/nondissipative transport limits future innovations.For contact sizes of the order of a few Fermi wavelengths F , well defined modes ͑channels͒ appear associated with the transversal confinement of electrons. For this situation, the conductance G is given by the Landauer formula G = G 0 ͚ n=1 N T n , where G 0 =2e 2 / h is the conductance quantum ͑e being the electron charge and h Planck's constant͒, T n is the transmission probability of the nth channel, and N is the number of propagating modes with energies below the Fermi energy. 2 It has been shown that the number of conducting channels is determined by the number of valence electrons of the respective chemical element. 3 For monovalent noble metals such as Cu, Ag and Au, the transmission probability T has been estimated to be approximately equal to 1 ͑i.e., each noble-metal atom contact contributes with G 0 to the conductance value 4,5 ͒. But for monovalent alkali metals or polyvalent chemical species, single-atom contact studies revealed that this channel transmittivity can have a result smaller than one. 3,6,7 Nowadays, there exist several experimental techniques to characterize the electronic transport through nanocontacts. Among them, the measurement of the conductance histogram during nanocontact breakages 8-10 is one of the most used. By putting in contact two opposite electrodes and then separating them, one observes a stepwise decrease in the electrical conductance ͑i.e., a conductance scan͒, until the breakpoint is reached. [11][12][13][14] It has been shown that each scan of the conductance dependence on the electrode retraction differs from one another, since the nanocontact structural evolutions during breakages are not identical. 15 Notwithstanding for fixed experimental parameter conditions ͑such as temperature and applied voltage...