The development of universal anode materials with superlative electrochemical performance poses a great challenge for rechargeable alkali metal (AM) ion battery technologies. In the present work, the viability of the gapless Dirac t-BN (tetragonal boron nitride) monolayer as a lightweight binder-free anode has been systematically evaluated via comprehensive first-principles calculations. Aside from the desirable electronic conductivity, the t-BN monolayer exhibits an excellent ionic conductivity as well due to its moderate affinity for Li, Na, and K atoms with favorable in-plane barriers of 0.36, 0.18, and 0.19 eV, respectively. Meanwhile, the presence of B4N4 octagons allows the AM atoms to penetrate through the t-BN monolayer. Excitingly, the host material delivers an ultrahigh specific capacity up to 1080 mA h g-1 for Li, 5400 mA h g-1 for Na, and 2160 mA h g-1 for K in the wake of low mean open-circuit voltages of 0.033, 0.203, and 0.300 V at the half-cell level. According to the standard hydrogen electrode methodology, the energy densities are forecasted to be as large as 3240, 13500, and 5680 mW h g-1 for Li, Na, and K ion batteries, respectively, with robust thermal stability up to at least 400 K. The safety and cycling durability of the t-BN monolayer are jointly corroborated via the moderate mechanical strengths and ab initio molecular dynamics simulations at the maximum intercalated states, as well as via the small lattice changes and its ultrahigh tolerable ultimate tensile strain. These findings unambiguously promise that the t-BN monolayer can serve as an appealing candidate for anode applications in AM ion batteries.