This work examines the release of a model water- soluble compound from electrospun polymer nanofiber assemblies. Such release attracts attention in relation with biomedical applications, such as controlled drug delivery. It is also important for stem cell attachment and differentiation on biocompatible electrospun nanofiber scaffolds containing growth factors, which have been encapsulated by means of electrospinning. Typically, the release mechanism has been attributed to solid-state diffusion of the encapsulated compound from the fibers into the surrounding aqueous bath. Under this assumption, a 100% release of the encapsulated compound is expected in a certain (long) time. The present work focuses on certain cases where complete release does not happen, which suggests that solid-state diffusion may not be the primary mechanism at play. We show that in such cases the release rate can be explained by desorption of the embedded compound from nanopores in the fibers, or from the outer surface of the fiber in contact with the water bath. After release, the water-soluble compound rapidly diffuses in water, whereas a release rate is determined by the limiting desorption stage. A model system of Rhodamine 610 fluorescent dye embedded in electrospun monolithic Poly(methylmethacrylate) PMMA or Poly(caprolactone) PCL nanofibers, or in nanofibers electrospun from PMMA/PCL blends, or in core/shell PMMA/PCL nanofibers is studied. Both the experimental results and theory point at the above-mentioned desorption-related mechanism and the predicted characteristic time, release rate, and effective diffusion coefficient agree fairly well with the experimental data. A practically important outcome of this surface release mechanism is that only the compound on the fiber and pore surfaces can be released, whereas the material encapsulated in the bulk cannot be freed within the time scales characteristic of the present experiments (days to months). Consequently, in such cases complete release is impossible. We also demonstrate how the release rate can be manipulated by the polymer content and molecular weight affecting nanoporosity and the desorption enthalpy, as well as by the nanofiber structure (monolithic fibers, fibers from polymer blends and core-shell fibers). In particular, it is shown that by manipulating the above parameters, release times from tens of hours to months can be attained.