Surfaces and objects surround us, and touching them is integral to everyday life. Pathogen contaminated surfaces (fomites) are known to transmit diseases. However, little is known about the ways and speed at which surfaces become contaminated. We found that under certain conditions, the number of contaminated surfaces grows logistically, corresponding to possible rapid transmission of infection. In such a surface network, pathogen can be transmitted great distances quickly-as far as people move. We found that the surface contamination network in aircraft cabins exhibits a community structure, with small communities connected by the aisle seatback surfaces and toilets, which are high-touch surfaces. In less than two to three hours, most high-touch surfaces in the cabin are contaminated, and within five to six hours nearly all touchable surfaces are contaminated. During short haul flight, aisle passengers have higher fomite exposure. This closely matches the spatial infection pattern of one reported inflight norovirus outbreaks. Our model is generally applicable to other crowded settings. The commonly repeated advice to "wash hands frequently" may be replaced in future by more strategic advice such as "clean surfaces right now", or advice based on who should wash their hands, and when.