  In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of
random planar graph. As a particular case, that model yields tessellations with
only T-vertices (T-tessellations). Using a similar approach involving Poisson
lines, a new model of random T-tessellations is proposed. Campbell measures,
Papangelou kernels and Georgii-Nguyen-Zessin formulae are translated from point
process theory to random T-tessellations. It is shown that the new model shows
properties similar to the Poisson point process and can therefore be considered
as a completely random T-tessellation. Gibbs variants are introduced leading to
models of random T-tessellations where selected features are controlled. Gibbs
random T-tessellations are expected to better represent observed tessellations.
As numerical experiments are a key tool for investigating Gibbs models, we
derive a simulation algorithm of the Metropolis-Hastings-Green family.
