  For a class of cell division processes, generating tessellations of the
Euclidean space $\mathbb{R}^d$, spatial consistency is investigated. This
addresses the problem whether the distribution of these tessellations,
restricted to a bounded set $V$, depends on the choice of a larger region
$W\supset V$ where the construction of the cell division process is performed.
This can also be understood as the problem of boundary effects in the cell
division procedure. In Nagel and Wei\ss\ (2005) it was shown that the STIT
tessellations are spatially consistent There were hints that the STIT
tessellation process might be the only translation-invariant cell division
process that has such a consistency property. In the present paper it is shown
that, within a reasonable wide class of cell division processes, the STIT
tessellations are the only ones that are consistent.
