  We define the decomposition property for partial actions of discrete groups
on $C^*$-algebras. Decomposable partial systems appear naturally in practice,
and many commonly occurring partial actions can be decomposed into partial
actions with the decomposition property. For instance, any partial action of a
finite group is an iterated extension of decomposable systems.
  Partial actions with the decomposition property are always globalizable and
amenable, regardless of the acting group, and their globalization can be
explicitly described in terms of certain global sub-systems. A direct
computation of their crossed products is also carried out. We show that partial
actions with the decomposition property behave in many ways like global actions
of finite groups (even when the acting group is infinite), which makes their
study particularly accessible. For example, there exists a canonical faithful
conditional expectation onto the fixed point algebra, which is moreover a
corner in the crossed product in a natural way. (Both of these facts are in
general false for partial actions of finite groups.) As an application, we show
that freeness of a topological partial action with the decomposition property
is equivalent to its fixed point algebra being Morita equivalent to its crossed
product. We also show by example that this fails for general partial actions of
finite groups.
