  The liquid-liquid critical point scenario of water hypothesizes the existence
of two metastable liquid phases---low-density liquid (LDL) and high-density
liquid (HDL)---deep within the supercooled region. The hypothesis originates
from computer simulations of the ST2 water model, but the stability of the LDL
phase with respect to the crystal is still being debated. We simulate
supercooled ST2 water at constant pressure, constant temperature and constant
number of molecules N for N<=729 and times up to 1000 ns. We observe clear
differences between the two liquids, both structural and dynamical. Using
several methods, including finite-size scaling, we confirm the presence of a
liquid-liquid phase transition ending in a critical point. We find that the LDL
is stable with respect to the crystal in 98% of our runs (we perform 372 runs
for LDL or LDL-like states), and in 100% of our runs for the two largest system
sizes (N=512 and 729, for which we perform 136 runs for LDL or LDL-like
states). In all these runs tiny crystallites grow and then melt within 1000 ns.
Only for N<=343 we observe six events (over 236 runs for LDL or LDL-like
states) of spontaneous crystallization after crystallites reach an estimated
critical size of about 70+/-10 molecules.
