We have studied the ground state structure of quantum strips within the local spin-density approximation, for a range of electronic densities between 5 104 and 2 106cm−1 and several strengths of the lateral confining potential. The results have been used to address the conductance G of quantum strips. At low density, when only one subband is occupied, the system is fully polarized and G takes a value close to 0.7 2e2 /h, decreasing with increasing electron density in agreement with experiments. At higher densities the system becomes paramagnetic and G takes a value near 2e2 /h, showing a similar decreasing behavior with increasing electron density. In both cases, the physical parameter that determines the value of the conductance is the ratio K/K0 of the compressibility of the system to the free one.