We present a novel approach to study the three-dimensional network structure of paper. In the KCL-PAKKA simulation model, the porous sheet structure is compiled from the different papermaking raw materials, fibres, fillers and fines. The model geometry is simplified in order to enable effective numerical experiments with arbitrary composition and layering. The KCL-PAKKA model gives realistic predictions for many paper properties . In this paper we describe the cross-over that occurs with increasing grammage from a thin strictly two-dimensional network to a thick layered networks . According to our simulations the cross-over occurs at low grammages, around 20 – 30 g/m2, for papers made of stifffibres (e.g . mechanical pulp) and at higher grammages, 40 – 80 g/m2, for flexible fibres (e .g . beaten kraft) . We discuss the statistical properties of the three-dimensional but layered random fibre network, particularly the bonding degree and pore geometry . In thick networks the pore geometry . i s isomorphic and only the length scale of the pores depends on fibre properties.