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Let $(M,g)$ be a two dimensional compact Riemannian manifold of genus$g(M)>1$. Let $f$ be a smooth function on $M$ such that $$f \ge 0, \quadf\not\equiv 0, \quad \min_M f = 0. $$ Let $p_1,\ldots,p_n$ be any set of pointsat which $f(p_i)=0$ and $D^2f(p_i)$ is non-singular. We prove that for allsufficiently small $\lambda>0$  there exists a family of "bubbling" conformal metrics$g_\lambda=e^{u_\lambda}g$ such that their Gauss curvature is given by thesign-changing function $K_{g_\lambda}=-f+\lambda^2$. Moreover, the family$u_\lambda$ satisfies $$u_\lambda(p_j) = -4\log\lambda -2\log \left (\frac1{\sqrt{2}} \log \frac 1\lambda \right ) +O(1)$$ and$$\lambda^2e^{u_\lambda}\rightharpoonup8\pi\sum_{i=1}^{n}\delta_{p_i},\quad\mbox{as }\lambda \to 0,$$ where $\delta_{p}$ designates Dirac mass at thepoint $p$.

Large Conformal metrics with prescribed sign-changing Gauss curvature