We report on the transport properties of novel carbon nanostructures made of partially unzipped carbon nanotubes, which can be regarded as a seamless junction of a tube and a nanoribbon. We find that graphene nanoribbons act at certain energy ranges as perfect valley filters for carbon nanotubes, with the maximum possible conductance. Our results show that a partially unzipped carbon nanotube is a magnetoresistive device, with a very large value of magnetoresistance. We explore the properties of several structures combining nanotubes and graphene nanoribbons, demonstrating that they behave as optimal contacts for each other, and opening a new route for the design of mixed graphene-nanotube devices.