The behaviour of the transients due to the model of the growth of right-circular cones is fully explored and compared to that of hemispheroids. The conditions that justify the use of the limiting forms of the transient equations for the so-called 'instantaneous' and 'progressive' nucleation processes are evaluated. Nucleation rates obtained from the fit of the recorded transients to the generalised equations derived for both growth models are compared. It is shown that even in those cases where electrocrystallisation proceeds via nucleation and growth of hemispheroids, analysis of the transients according to the model of the growth of cones results in estimates of nucleation rates which differ by at most a factor of three, and in most cases are as close as half the actual value.