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Transient electrospray atomization in the cone-jet mode is investigated by means of numerical simulations. The case of electrospray jets growing from a liquid dripping from a capillary is studied. For the characterization of the process, a particular electrospray configuration is considered for which experimental validation data are available. The droplet charge, radius and their correlations are computed for different flow rates, for transient as well as for steady state electrosprays. It is found that the charge-radius correlation of primary droplets in the initial phase of the electrospray follows a power law similar to the universal scaling law for the first atomization. However, as the electrospray develops towards steady state, the electrospray characteristics changes. The power exponent of the charge-radius correlation is still independent from the flow rate. However, this exponent deviates from that of early stage electrospray. In particular, simulations show that at steady state, the charge of primary electrospray droplets is directly proportional to their volume.