  Given a connected, oriented, complete, finite area hyperbolic surface $X$ of
genus $g$ with $n$ punctures, Mirzakhani showed that the number of
multi-geodesics on $X$ of total hyperbolic length $\leq L$ in the mapping class
group orbit of a given simple or filling closed multi-curve is asymptotic as $L
\to \infty$ to a polynomial in $L$ of degree $6g-6+2n$. We establish
asymptotics of the same kind for countings of multi-geodesics in mapping class
group orbits of simple or filling closed multi-curves that keep track of the
hyperbolic lengths of individual components, proving and generalizing a
conjecture of Wolpert. In the simple case we consider more precise countings
that also keep track of the class of the multi-geodesics in the space of
projective measured geodesic laminations. We provide a unified geometric and
topological description of the leading terms of the asymptotics of all the
countings considered. Our proofs combine techniques and results from several
papers of Mirzakhani as well as ideas introduced by Margulis in his thesis.
