We have recently shown that molecular hydrogen generation from organic matter occurs at high maturity levels (vitrinite reflectance 3–5%) in Lower Cretaceous shales of the Songliao Basin. To evaluate and extend these implications to a wider range of source rock types and organofacies, we report on two Paleozoic maturity suites from Australia, namely the Permian Patchawarra Formation (fluviodeltaic; Type-III; Cooper Basin) and the middle Cambrian Arthur Creek Formation (marine; Type-II; Georgina Basin), and additional mature marine source rocks from Europe and the USA.It can be inferred from high resolution mass spectrometry that rapid growth of aromatic ring systems is the major pathway for the formation of thermogenic molecular hydrogen from all organic matter types. Extensive open system pyrolysis experiments indicate that the main generation pulse occurs in the vitrinite reflectance range 3.5–5.0%. Kinetic parameters were constructed by subtracting the hydrogen associated with hydrocarbon formation from total hydrogen in the open-system experiments via adjustment factors defined by the relative yields of CH4 and H2. A cumulative H2 potential of 20 mg/g TOC is found with maximum rates of generation that are sufficient for feeding the deep biosphere. Back of the envelope calculations indicate ∼3.5E+10 tonnes of in-place accessible H2 globally, which is an order of magnitude lower than in-place shale gas resource estimates. Regionally, inferred here for the Patchawarra Formation in the Nappamerri Trough (Cooper Basin), yields per unit rock volume resemble those of economic shale gas in the Barnett Shale, Fort Worth Basin, USA.Organic particles are, at the SEM-scale (>30 nm), barren of secondary porosity in the case of terrigenous samples at all maturity stages, but show sponge-like porosity in the investigated marine source rocks exhibiting vitrinite reflectance >∼2.0%. Presence of such meso- and macropores is crucial for H2 storage in marine shales, as microporosity (<2 nm) yielding sorptive storage space for H2, is usually much higher in mature terrigenous kerogens.