Splitting a single droplet into two unequal portions using a microfluidic T-junction has been an important functional feature of many modern lab-on-a-chip devices. A recent study introduced a general criterion for asymmetric droplet break-up in the range of intermediate Capillary numbers. The current work attempts to analyze, in more details, the different underlying mechanisms governing the asymmetric break-up process. In particular, this work focuses on the relationship between the break-up mechanism versus the splitting ratio of the daughter droplets. CFD simulation is used to closely monitor the effect of different fluid properties on the evolution of droplet break-up process. The splitting ratio under different flow conditions is characterized. Four mechanisms for primary droplet break-up are defined as follows: break-up with permanent obstruction, unstable break-up, breakup with tunnels and non-breakup. In particular, the main focus of this study is on the unstable break-up mechanisms where is very likely results to a much-deviated splitting ratio. Typically, yet unexpectedly, the resulting splitting ratio is often larger than the pressure gradient ratio in the T-junction. However, the two ratios are approximately equals to each other under a limited set of flow conditions. It has been observed that the splitting ratio could be more than double the pressure gradient ratio of the T-junction. The break-up is observed to be in the permanent obstruction mode if the splitting ratio is about the same magnitude as the pressure gradient ratio. The effects of the T-junction geometry on the break-up will also be examined.