  We discuss the geometry of trees endowed with a causal structure using the
conventional framework of equilibrium statistical mechanics. We show how this
ensemble is related to popular growing network models. In particular we
demonstrate that on a class of afine attachment kernels the two models are
identical but they can differ substantially for other choice of weights. We
show that causal trees exhibit condensation even for asymptotically linear
kernels. We derive general formulae describing the degree distribution, the
ancestor-descendant correlation and the probability a randomly chosen node
lives at a given geodesic distance from the root. It is shown that the
Hausdorff dimension d_H of the causal networks is generically infinite.
