Hydrogen represents a versatile energy carrier with net zero end use emissions. Power-to-Liquid (PtL) includes the combination of hydrogen with CO2 to produce liquid fuels and satisfy mostly transport demand. This study assesses the role of these pathways across scenarios that achieve 80-95% CO2 reduction by 2050 (vs. 1990) using the JRC-EU-TIMES model. The gaps in the literature covered in this study include a broader spatial coverage (EU28 +) and hydrogen use in all sectors (beyond transport). The large uncertainty in the possible evolution of the energy system has been tackled with an extensive sensitivity analysis. 15 parameters were varied to produce more than 50 scenarios. Results indicate that parameters with the largest influence are the CO2 target, the availability of CO2 underground storage and the biomass potential. Hydrogen demand increases from 7 mtpa today to 20-120 mtpa (2.4-14.4 EJ/yr), mainly used for PtL (up to 70 mtpa), transport (up to 40 mtpa) and industry (25 mtpa). Only when CO2 storage was not possible due to a political ban or social acceptance issues, was electrolysis the main hydrogen production route (90% share) and CO2 use for PtL became attractive. Otherwise, hydrogen was produced through gas reforming with CO2 capture and the preferred CO2 sink was underground. Hydrogen and PtL contribute to energy security and independence allowing to reduce energy related import cost from 420 bln(sic)/yr today to 350 or 50 bln(sic)/yr for 95% CO2 reduction with and without CO2 storage. Development of electrolyzers, fuel cells and fuel synthesis should continue to ensure these technologies are ready when needed. Results from this study should be complemented with studies with higher spatial and temporal resolution. Scenarios with global trading of hydrogen and potential import to the EU were not included.