  The seminal papers of Edmonds \cite{Egy}, Nash-Williams \cite{NW} and Tutte
\cite{Tu} have laid the foundations of the theories of packing arborescences
and packing trees. The directed version has been extensively investigated,
resulting in a great number of generalizations. In contrast, the undirected
version has been marginally considered. The aim of this paper is to further
develop the theories of packing trees and forests. Our main result on graphs
characterizes the existence of a packing of $k$ forests, $F_1, \ldots, F_k$, in
a graph $G$ such that each vertex of $G$ belongs to exactly $h$ of the forests,
and in addition, each $F_i$ has between $\ell(i)$ and $\ell'(i)$ connected
components and the total number of connected components in the packing is
between $\alpha$ and $\beta$. Finally, we extend this result to hypergraphs and
dypergraphs, the latter giving a generalization of a theorem of B\'erczi and
Frank \cite{BF3}.
