We prove the uniform stability of some smooth DM stacks obtained by further ramifying the moduli stack of stable curves over the Deligne-Mumford boundary divisor and apply this construction to prove that most of the complex projective surfaces proposed by Bogomolov and Katzarkov in 1997 as counter examples to the Shafarevich conjecture on holomorphic convexity do satisfy this statement. Joint work with Louis Funar. arXiv:2112.06726 [math.AG].