This work is a continuation of two previous papers of a series, in which we examined the pulse-width statistics of normal radio pulsars. In the first paper, we compiled the largest ever data base of pulsars with interpulses in their mean profiles. In the second one, we confirmed the existence of the lower boundary in the scatter plot of core component pulse-widths versus the pulsar period W50 ∼ 2.°5 P−0.5, first discovered by Rankin using a much smaller number of interpulse cases. In this paper, we show that the same lower boundary also exists for the conal profile components. Rankin proposed a very simple method of estimation of the pulsar inclination angle based on comparing the width W50 of its core component with the period-dependent value of the lower boundary. We claim that this method can be extended to conal components as well. To explain the existence of the lower boundary, Rankin proposed that the core emission originates at or near the polar cap surface. We demonstrated clearly that no coherent pulsar radio emission can originate at altitudes lower than 10 stellar radii, irrespective of the actual mechanism of coherence. We argue that the lower boundary reflects the narrowest angular structures that can be distinguished in the average pulsar beam. These structures represent the core and the conal components in mean pulsar profiles. The P−0.5 dependence follows from the dipolar nature of the magnetic field lines in the radio emission region, while the numerical factor of about 2.°5 reflects the curvature radius of a non-dipolar surface magnetic field in the partially screened gap above the polar cap, where dense electron–positron plasma is created. Both the core and conal emission should originate at altitudes of about 50 stellar radii in a typical pulsar, with a possibility that the core beam is emitted at slightly lower heights than the conal ones.