Abstract: Asymmetric T-junctions have recently emerged as a promising tool in microfluidics. However, previous studies of the droplet formation mechanism are largely limited to symmetric T-junctions. In this work, the droplet formation in universal T-junctions, including both symmetric and asymmetric T-junctions, is investigated by a three-dimensional color-gradient lattice Boltzmann model. A three-dimensional color-conserving boundary condition is developed to model fluid-surface interactions, which suppresses the spurious velocities near the contact lines and improves numerical accuracy. Model verification is conducted by the partial wetting test and the droplet formation in a symmetric T-junction. Then, an in-depth study is performed for universal T-junctions. In both symmetric and asymmetric T-junctions, the droplet length is linearly dependent on flow rate ratio at low capillary number, and the droplet formation successively undergoes squeezing, dripping and jetting regimes as the capillary number increases. By investigating the local pressure and velocity field, we find that the upstream pressure and viscous force respectively dominates the droplet formation in squeezing and dripping regimes. In squeezing regime, the pressure fluctuates significantly, and the fluctuation amplitude and frequency decrease with the channel width ratio; while in dripping regime, the pressure fluctuation is negligibly small, and the viscous force is found to decrease with the channel width ratio. Consequently, the droplet size increases with the channel width ratio in both regimes. In addition, the viscosity ratio and surface wettability are found to be influential to the formation regime, droplet shape and size for various channel width ratios and capillary numbers, and play important roles in droplet formation.