We study the production of longitudinally polarized L baryons in single-spin p p collisions at BNL RHIC and DESY HERA-N as a means of determining the spin-dependent L fragmentation functions. It is shown that a measurement of the rapidity distribution of the L's would provide an excellent way of clearly discriminating between various recently suggested sets of polarized L fragmentation functions that are all compatible with present e 1 e 2 data. We also address the main theoretical uncertainties, which appear to be well under control. [S0031-9007(98)06651-4] PACS numbers: 13.88. + e, 13.85. Ni, 13.87.Fh, 14.20.Jn The understanding of spin-dependent deep-inelastic scattering (DIS) processes in terms of QCD-evolved polarized parton distributions Df͑x, Q 2 ͒ ͑ f q,q, g͒ is still far from being satisfactory, despite significant experimental and theoretical progress over the past few years. In particular, the angular momentum component of the proton's spin and the polarized gluon density Dg͑x, Q 2 ͒ remain almost completely unknown for the time being, and more experimental results are required.Studies of spin-transfer reactions could provide further invaluable and completely new insight into the field of "spin physics" and, in addition, might also yield a better understanding of the hadronization process. Such cross sections can be expressed as convolutions of perturbatively calculable partonic spin-transfer cross sections with certain sets of parton distributions and fragmentation functions, whose scale dependence is completely predicted by QCD once a suitable nonperturbative input at some reference scale has been determined by data. To obtain a nonvanishing twist-2 spin-transfer asymmetry, the measurement of the polarization of one outgoing particle is obviously required, in addition to having a polarized beam or target. This certainly provides a great experimental challenge. L-baryons are particularly suited for such studies due to the self-analyzing properties of their dominant weak decay L ! pp 2 , and recent results on L production reported from large electron-positron collider (LEP) [1] have demonstrated the experimental feasibility of successfully reconstructing the L spin.In [2] a first attempt was made to determine the spindependent L fragmentation functions by analyzing these LEP data [1] in leading and next-to-leading order QCD, using the results of a preceding study of unpolarized L fragmentation functions. Unfortunately it turned out, however, that the available LEP data, all obtained on the Z resonance and, hence, sensitive only to the flavor nonsinglet part of the cross section, cannot even sufficiently constrain the valence fragmentation functions for all flavors.Rather different, but all physically conceivable, scenarios adopted for the input valence distributions appear to describe the data equally well, and for the "unfavored" sea quark and gluon fragmentation functions one has to fully rely on mere assumptions. Clearly, further measurements of other helicity transfer processes are required to ...