  We introduce and study the complexity of Path Packing. Given a graph $G$ and
a list of paths, the task is to embed the paths edge-disjoint in $G$. This
generalizes the well known Hamiltonian-Path problem.
  Since Hamiltonian Path is efficiently solvable for graphs of small treewidth,
we study how this result translates to the much more general Path Packing. On
the positive side, we give an FPT-algorithm on trees for the number of paths as
parameter. Further, we give an XP-algorithm with the combined parameters
maximal degree, number of connected components and number of nodes of degree at
least three. Surprisingly the latter is an almost tight result by runtime and
parameterization. We show an ETH lower bound almost matching our runtime.
Moreover, if two of the three values are constant and one is unbounded the
problem becomes NP-hard.
  Further, we study restrictions to the given list of paths. On the positive
side, we present an FPT-algorithm parameterized by the sum of the lengths of
the paths. Packing paths of length two is polynomial time solvable, while
packing paths of length three is NP-hard. Finally, even the spacial case EPC
where the paths have to cover every edge in $G$ exactly once is already NP-hard
for two paths on 4-regular graphs.
