  The STIT tessellation process was introduced and examined by Mecke, Nagel and
Wei{\ss}; many of its main characteristics are contained in a paper published
by Nagel and Wei{\ss} in 2005. In a paper published in 2010, Mecke introduced
another process in discrete time. With a geometric distribution whose parameter
depends on the time, he reaches a continuous-time model. In his Conjecture 3,
he assumed this continuous-time model to be equivalent to STIT. In the present
paper, that conjecture is proven. An interesting relation arises to a
continuous-time version of the equally-likely model classified by Cowan in
2010. This will also clarify how Mecke's model works as a process in continuous
time.
