  In this paper we continue to explore "hybrid" quantum circuit models in
one-dimension with both unitary and measurement gates, focussing on the
entanglement properties of wavefunction trajectories at long times, in the
steady state. We simulate a large class of Clifford circuits, including models
with or without randomness in the unitary gates, and with or without randomness
in the locations of measurement gates, using stabilizer techniques to access
the long time dynamics of systems up to 512 qubits. In all models we find a
volume law entangled phase for low measurement rates, which exhibits a
sub-dominant logarithmic behavior in the entanglement entropy, $S_A = {\alpha}
\ln |A| + s|A|$, with sub-system size $|A|$. With increasing measurement rate
the volume law phase is unstable to a disentangled area law phase, passing
through a single entanglement transition at a critical rate of measurement. At
criticality we find a purely logarithmic entanglement entropy, $S_A =
{\alpha}(p_c) \ln|A|$, a power law decay and conformal symmetry of the mutual
information, with exponential decay off criticality. Various spin-spin
correlation functions also show slow decay at criticality. Critical exponents
are consistent across all models, indicative of a single universality class.
These results suggest the existence of an effective underlying statistical
mechanical model for the entanglement transition. Beyond Clifford circuit
models, numerical simulations of up to 20 qubits give consistent results.
