In the early stages of the diffusion-controlled growth of electrodeposits, two independent processes are identified to simultaneously contribute towards the continual fall of the rate of crystal growth with the passage of time. One is the gradual reduction with time of the concentration gradient of the depositing species, a process successfully dealt by the Fick's Laws of diffusion. The other is the successive overlap of the diffusion zones, which together with the progressive coverage of the electrode surface by the growth centres, gradually transforms the flow configuration of ions from a radial mode to a linear stance. It is shown for the first time that all of the previously postulated current-time transients (CTTs) account only for the first of these processes. The previously postulated CTTs are divided in the present paper into two categories, those pertaining to the growth of cones, and those pertaining to the growth of hemispheres. By formulating the CTTs associated with the growth of cones, we show that the most cited, and certainly the most utilized CTT equation in the analysis of the recorded transients, fall into this category despite the contrary assertions. The actual forms, as well as the kinetics of the CTTs associated with the growth of cones, are shown to be not very dissimilar from those which are derived in the present paper for the diffusion controlled growth of hemispherical centres. (c) 2005 Elsevier B.V. All rights reserved.