The properties of hydrogen at high pressure have wide implications in astrophysics and high-pressure physics. Its phase change in the liquid is variously described as a metallization, H2-dissociation, density discontinuity or plasma phase transition. It has been tacitly assumed that these phenomena coincide at a first-order liquid-liquid transition (LLT). In this work, the relevant pressure-temperature conditions are thoroughly explored with first-principles molecular dynamics. We show there is a large dependency on exchange-correlation functional and significant finite size effects. We use hysteresis in a number of measurable quantities to demonstrate a first-order transition up to a critical point, above which molecular and atomic liquids are indistinguishable. At higher temperature beyond the critical point, H2-dissociation becomes a smooth cross-over in the supercritical region that can be modelled by a pseudo-transition, where the H2→2H transformation is localized and does not cause a density discontinuity at metallization. Thermodynamic anomalies and counter-intuitive transport behavior of protons are also discovered even far beyond the critical point, making this dissociative transition highly relevant to the Supplementary Material. Results of dimer-dimer bond-length distribution (DDLD) calculations, comparison between PBE and vdW-DF results, the thermodynamic modelling of pseudo-transition and phase boundaries, calculated isotherms (equation of state, EOS), transient clusters and their lifetime and charge state, the angular distribution function of H3 clusters, mixing of H and H2 liquid, thermal fluctuation analysis, isotope effect, finite size effects, and the assessment of proton selfdiffusivity and viscosity.