The present invention relates to structures that contain one or more fiber and/or nanofiber structures where such structures can be formed on a wide variety of structures or surfaces (e.g., asperities, flat surfaces, angled surface, hierarchical structures, etc.). In one embodiment, the present invention relates to a process for forming one or more fibers, nanofibers or structures made therefrom on a wide variety of structures or surfaces (e.g., asperities, flat surfaces, angled surface, hierarchical structures, etc.). In another embodiment, the present invention relates to a process for forming one or more fibers, nanofibers or structures made therefrom on a wide variety of structures or surfaces (e.g., asperities, flat surfaces, angled surface, hierarchical structures, etc.) where such fibers and/or structures are designed to sequester, carry and/or encapsulate one or more substances. In still another embodiment, the present invention relates to structures that contain one or more fiber and/or nanofiber structures on asperities where the nanofiber and/or fiber structures are designed to sequester, carry and/or encapsulate one or more substances.