  It is shown that the hadronic dissociation of space-like $(Q^2>0)$ photons
can be directly probed by performing measurements in the fragmentation region
of transversely polarized and unpolarized proton beams at the electron-proton
collider HERA. Measurements of momentum-distributions in the
photon-fragmentation region in normal and in LRG (large rapidity gap) events
are also suggested --- especially when the scattered proton or neutron in the
proton-beam direction is tagged. It is pointed out that such distributions can
yield useful information on the mechanisms of hadronic fragmentation in
general, and answer the following questions in particular: Is the well-known
hypothesis of limiting fragmentation (HFL) valid in color-exchange, in
flavor-exchange, or only in vacuum-quantum-number-exchange processes ?
