The helical Cerenkov effect results from the helical electron motion in a medium with a rather strong magnetic field B. However, at the same radiation angle and the same frequency at which the helical Cerenkov effect is observed one will see harmonic radiation if the parallel (with respect to the magnetic field B) electron velocity components are above and below the helical Cerenkov effect threshold. Increase in the strength in B decreases the number of harmonics at both sides of the helical Cerenkov effect threshold. The radiation frequency dependent asymptotic limit is achieved, by definition, when the number of harmonics, regardless whether occurring below or above the helical Cerenkov effect threshold, is reduced to just the first one. In the visible spectrum and for silica aerogel as a medium such as asymptotic limit already happens at B approximately equal to 100 T. There is also a universal frequency dependent asymptotic limit when, regardless of the medium and the radiation angle, no harmonic radiation can occur and only the helical Cerenkov radiation should exist. In the visible spectrum, we argue, this should happen at B approximately equal to 104 T. For magnetic fields that are even stronger than this, as for example the ones that can be found in neutron stars (pulsars), B < 108 T, not only that harmonic radiation does not appear but the helical Cerenkov effect degenerates into a form of the ordinary Cerenkov effect, whose angular dependence, however, is determined with respect to the direction of the magnetic field rather than the initial electron velocity.