We have investigated the formation and the morphology of carbon deposit on the cathode, after arc discharge between two graphite electrodes immersed in liquid nitrogen. We show that the deposit is mainly composed of disordered carbon structures at the bottom and at the external part of the deposit, forming like a bowl, whereas randomly oriented carbon nanotubes (CNTs) aggregated as pillars are found at the center of the deposit. The spatial distribution of the two kinds of structures in the deposit, the size and the sharpness of the CNT pillars are found to depend both on the applied voltage and the current values used for the arc discharge. A correlation between the plasma temperature field and the morphology of the deposit is reported.