Transformations of water's high density amorph (HDA) to low density amorph (LDA) and of LDA's to cubic ice (Ic) have been studied by in situ thermal conductivity kappa measurements at high pressures. The HDA to LDA transformation is unobservable at p of 0.07 GPa, indicating that, for a fixed heating rate, an increase in pressure increases the temperature of HDA to LDA transformation and decreases that of LDA to ice Ic, causing thereby the two transformations to merge, and HDA appears to convert directly to ice Ic. Thus either LDA forms but converts extremely rapidly to ice Ic, or LDA does not form. At a fixed p and T, in the range of pressure amorphization of hexagonal ice, kappa continues to decrease with time. Therefore, the amorphization of ice Ih is kinetically controlled. When HDA at 1 GPa was heated from 130 to 157 K and densified to very HDA, its kappa increased by 3%. Our findings and a scrutiny of earlier reports show that a reversible transition between HDA and LDA does not occur at similar to135 K and similar to0.2 GPa. Since there is no unique HDA, it is difficult to justify the conjecture for a second critical point for water. (C) 2004 American Institute of Physics.