Following their discovery in the late nineteenth century, the papyri of the Zenon archive were divided between numerous musuems, institutions and collections, including the University of Michigan, Columbia University, the Societa Italiana per la Ricerca dei Papiri, and the British and Cairo Museums. For more information on the archive, you can visit the Zenon section of the Leuven Homepage of Papyrus Archives and Collection.
Many of the texts of the Zenon Papyri are online. You can view all of the Zenon texts in the APIS database (which includes all those held by the University of Michigan, Duke University, and Columbia University). You can also search online for Zenon papyri in The Heidelberg Collection.