Models of three-dimensional space filling based on growth of two-dimensional sheets are proposed. Beginning from planar Eden-style growth of sheets, additional growth modes are introduced. These enable the sheets to form layered or disordered structures. The growth modes can also be combined. An off-lattice kinetic Monte Carlo-based computer algorithm is presented and used to study the kinetics of the new models and the resulting structures. It is possible to study space filling by two-dimensional growth in a three-dimensional domain with arbitrarily oriented sheets; the results agree with previously published models where the sheets are only able to grow in a limited set of directions. The introduction of a bifurcation mechanism gives rise to complex disordered structures that are of interest as model structures for the mesostructure of calcium silicate hydrate in hardened cement paste.