  Cohomology of affinoids does not behave well; often, this can be remedied by
making affinoids overconvergent. In this paper, we focus on dimension 1 and
compute, using analogs of pants decompositions of Riemann surfaces, various
cohomologies of affinoids. To give a meaning to these decompositions we modify
slightly the notion of $p$-adic formal scheme, which gives rise to the adoc (an
interpolation between adic and ad hoc) geometry. It turns out that cohomology
of affinoids (in dimension 1) is not that pathological. From this we deduce a
computation of cohomologies of curves without boundary (like the Drinfeld
half-plane and its coverings). In particular, we obtain a description of their
$p$-adic pro-\'etale cohomology in terms of de the Rham complex and the
Hyodo-Kato cohomology, the later having properties similar to the ones of
$\ell$-adic pro-\'etale cohomology, for $\ell\neq p$.
