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We investigate the electron emission from a sub-nm radius carbon tip, acting as electron emitter, which has a highly nonlinear Fowler-Nordheim plot. The traditional theories of field emission of Fowler and Nordheim and their later versions as well as that of thermionic emission by Richardson and Dushman are not applicable for such tips because of the high curvature indicating strong localization effects. The inapplicability of such theories in the case of field emission has been demonstrated in a recent publication of our’s1. In this work we analyse further I-V (current-voltage) data at higher voltages in which we can distinguish two more emission regions in addition to field emission: thermionic emission and space charge limited emission. Both these two regions are analysed with our new theory using wave functions with wavefronts that fit the emission area of the emitter tip. Good agreement with experiment is obtained whereas traditional theories show deviations from experiment which may be up to 6 orders of magnitude. Such agreement shows further the inadequacy of the traditional plane wave based theories.