The bulk properties and stochastic pore geometry of finite-thickness fiber webs are studied using a realistic model for the sedimentation of flexible fibers [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett.73, 3475 (1994)]. The resulting web structure is controlled by a dimensionless numberF=Tfwf/tf,whereTfis fiber flexibility,wffiber width, andtffiber thickness. The fiber length(≫wf,tf)is irrelevant. With increasing coveragec¯,a crossover occurs atc¯=c0≈1+2Ffrom a vacancy-controlled two-dimensional (2D) structure to a pore-controlled 3D structure. The 3D structures are isomorphic in that the pore dimensions are exponentially distributed, with the decay rate dependent only onF.©1997 American Institute of Physics.