  The article concerns the geometrical theory of general systems $\Omega$ of
partial differential equations in the \emph{absolute sense}, i.e., without any
additional structure and subject to arbitrary change of variables in the widest
possible meaning. The main result describes the composition series
$\Omega^0\subset\Omega^1\subset\cdots\subset\Omega$ where $\Omega^k$ is the
maximal system of differential equations "induced" by $\Omega$ such that the
solution of $\Omega^k$ depends on arbitrary functions of $k$ independent
variables (on constants if $k=0$). This is a~well--known result for the
particular case of underdetermined systems of ordinary differential equations.
Then $\Omega=\Omega^1$ and we have the composition series
$\Omega^0\subset\Omega^1=\Omega$ where $\Omega^0$ involves all first integrals
of $\Omega,$ therefore $\Omega^0$ is trivial (absent) in the controllable case.
The general composition series
$\Omega^0\subset\Omega^1\subset\cdots\subset\Omega$ may be regarded as
a~"multidimensional" controllability structure for the partial differential
equations.
  Though the result is conceptually clear, it cannot be included into the
common jet theory framework of differential equations. Quite other and
genuinely coordinate--free approach is introduced.
