  Causal Dynamical Triangulations (CDT), a candidate theory of nonperturbative
quantum gravity in 4D, turns out to have a rich phase structure. We investigate
the recently discovered bifurcation phase $C_b$ and relate some of its
characteristics to the presence of singular vertices of very high order. The
transition lines separating this phase from the "time-collapsed" $B$-phase and
the de Sitter phase $C_{dS}$ are of great interest when searching for physical
scaling limits. The work presented here sheds light on the mechanisms behind
these transitions. First, we study how the $B$-$C_b$ transition signal depends
on the volume-fixing implemented in the simulations, and find results
compatible with the previously determined second-order character of the
transition. The transition persists in a transfer matrix formulation, where the
system's time extension is taken to be minimal. Second, we relate the new
$C_b$-$C_{dS}$ transition to the appearance of singular vertices, which leads
to a direct physical interpretation in terms of a breaking of the homogeneity
and isotropy observed in the de Sitter phase when crossing from $C_{dS}$ to the
bifurcation phase $C_b$.
