  We study the disordered topological Anderson insulator in a 2-D (square not
strip) geometry. We first report the phase diagram of finite systems and then
study the evolution of phase boundaries when the system size is increased to a
very large $1120 \times 1120$ area. We establish that conductance quantization
can occur without a bulk band gap, and that there are two distinct scaling
regions with quantized conductance: TAI-I with a bulk band gap, and TAI-II with
localized bulk states. We show that there is no intervening insulating phase
between the bulk conduction phase and the TAI-I and TAI-II scaling regions, and
that there is no metallic phase at the transition between the quantized and
insulating phases. Centered near the quantized-insulating transition there are
very broad peaks in the eigenstate size and fractal dimension $d_2$; in a large
portion of the conductance plateau eigenstates grow when the disorder strength
is increased. The fractal dimension at the peak maximum is $d_2 \approx 1.5$.
Effective medium theory (CPA, SCBA) predicts well the boundaries and interior
of the gapped TAI-I scaling region, but fails to predict all boundaries save
one of the ungapped TAI-II scaling region. We report conductance distributions
near several phase transitions and compare them with critical conductance
distributions for well-known models.
