  We present a detailed analysis of a recently introduced version of Causal
Dynamical Triangulations (CDT) that does not rely on a distinguished time
slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its
geometric and causal properties, present details of the numerical set-up and
explain how to extract "volume profiles". Extensive Monte Carlo measurements of
the system show the emergence of a de Sitter universe on large scales from the
underlying quantum ensemble, similar to what was observed previously in
standard CDT quantum gravity. This provides evidence that the distinguished
time slicing of the latter is not an essential part of its kinematical set-up.
