The electromagnetically induced transparency (EIT) on the atomic D1 line of rubidium is studied using a nanometric-thin cell with atomic vapor column length in the range of L = 400-800 nm. It is shown that the reduction of the cell thickness by four orders as compared with an ordinary cm-size cell still allows to form an EIT resonance for L = λ = 794 nm with the contrast of up to 40%. Further reduction of thickness to L = λ/2 leads to significant reduction of EIT contrast, verifying that the key parameter for EIT in wavelength-scale-thickness cells is not the value of L itself but L/λ ratio. Remarkable distinctions of EIT formation in nanometric-thin and ordinary cells are demonstrated. Well-resolved splitting of the EIT resonance in a magnetic field for L = λ can be used for magnetometry with nanometric spatial resolution. The presented theoretical model well describes the observed results.