Triboelectric Nanogenerator (TENG) is a mechanical energy harvesting technology with the potential to autonomously power future wearable and portable electronics. Triboelectric charging is the major phenomenon governing the power generation and efficiency of a TENG. Studies on TENG, thus far, have focussed on the symmetric triboelectric charging with equal amounts of triboelectric charges with opposite polarities distributed on its two contact surfaces, especially for the purpose of theoretical modelling and simulations. Our work presents a fundamental study on the asymmetric triboelectric charging with unequal quantities of charges on TENG contact surfaces obtained through an external charging method, as an effective technique to enhance its power generation. For the first time, a theoretical model which can simulate the outputs of an asymmetrically charged TENG is derived using the distance-dependent electric field concept and experimentally verified, providing a detailed understanding of this phenomenon. The asymmetric charging is experimentally demonstrated to enhance the average power outputs of TENGs containing dissimilar contact surfaces (469% improvement) and identical contact surfaces (6076% improvement). Therefore, this study introduces a method to use identical triboelectric materials as TENG contact surfaces and generate comparable outputs to triboelectrically dissimilar materials, which significantly enhances the material range compatible for TENGs. Furthermore, we provide an insight into materials transfer characteristics between TENG contact surfaces and its impact on the non-linear external charging behaviour, revealing several crucial parameters which affect the efficiency and consistency of a TENG. Finally, this work elaborates on the TENG surface contaminations during experimental practices and the importance of TENG fabrication and characterisation procedures towards their long-term applications.