Let R_n be the radius of the largest empty ball centered at the origin of a branching random walk started from a Poisson random measure at time n. In 2002, Revesz proved that for a 1-dimensional critical branching Wiener process, R_n/n converges in law. For d=2 and d>2, he conjectured that R_n/\sqrt n and R_n will converge in law, respectively. Later, Hu confirmed the case of d>2 in 2005. In this talk, we intend to prove the case of d=2 in a general setting. Moreover, we shall also deal with some new cases eg. the offspring law is subcritical  or the offspring law has infinite variance, etc. Part of the work comes from the cooperation with Prof. Jie Xiong.