A comprehensive experimental investigation and theoretical description of liquid-gas pervaporative transport across nanoporous membranes is presented. Anodic alumina and track-etched membranes, featuring straight channels within a diameter range of 25-200 nm, were experimentally tested in pervaporation of liquid water, alcohols and hydrocarbons at various operation conditions. The pivotal role of the equilibrium saturation pressure of penetrants (varied from similar to 10 to similar to 50,000 Pa) on the membranes performance was exposed, while no significant influence of neither channel diameters nor membrane thickness was revealed. Pervaporative flux, exceeding 1.5<middle dot>10(-5) mol<middle dot>m(-2)<middle dot>s(-1)<middle dot>Pa-1 (similar to 10 kg<middle dot>m(-2)<middle dot>h(-1)<middle dot>atm(-1) for water at 60 degrees C), surpasses Knudsen permeability of the membranes, indicating liquid transport driven by Laplace pressure. However, it lies far below the theoretical Hertz-Knudsen limit for evaporating menisci, revealing heat transfer limitation. The study rivals a substantial temperature drop, reaching 30 degrees C at the evaporation plane. That is proportional to the square root of the saturation pressure of penetrants, as revealed by experimental results and theoretical description. It results in transport limitation with heat supply to the evaporation menisci, constrained especially at the membrane interfaces. Strong cooling of the evaporative plane suppresses pervaporative flux with diminishing local saturation pressure of penetrants. The provided description provides low relative deviation (<30 %) within the whole set of penetrants and membrane microstructures. It was successfully utilized for improving stability of nanoporous membranes in desalination pervaporation with deposition of highly permeable thin graphene oxide and MXene selective addlayers. Composite membranes reveal a slight lowering of the performance compared to the nanoporous substrates, while having a greatly enhanced long-term stability in pervaporative desalination with ions rejection.