I am working with closed degenarating hyperbolic Riemann surfaces, and I try to understand the compactification of the moduli space. Looking in different books, notably the one of Hummel, I now get a good intuition of what happens, but i have still not found a reference where this compactification is made precise in this setting. And I also look for a combinatorial description of what limit surface are possible? Even if I presume that all configuration are possible. Thank You.

I am working with closed degenerating hyperbolic Riemann surfaces, and I try to understand the compactification of the moduli space. Looking in different books, notably the one of Hummel, I now get a good intuition of what happens, but i have still not found a reference where this compactification is made precise in this setting. And I also look for a combinatorial description of what limit surface are possible? Even if I presume that all configuration are possible. Thank You.