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We study the fragmentation of a transversely polarized quark into a noncollinear (k_T not= 0) spinless hadron and the fragmentation of an unpolarizedquark into a non collinear transversely polarized spin 1/2 baryon. Thesenonperturbative properties are described by spin and k_T dependentfragmentation functions and are revealed in the observation of single spinasymmetries. Recent data on the production of pions in polarized semi-inclusiveDIS and long known data on Lambda polarization in unpolarized p-N processes areconsidered: these new fragmentation functions can describe the experimentalresults and the single spin effects in the quark fragmentation turn out to besurprisingly large.Comment: 5 pages + 2 eps figures, uses aipproc.sty and epsfig.sty. Talk  delivered by M. Anselmino at the "14th International Spin Physics Symposium",  SPIN2000, October 16-21, 2000, Osaka, Japa

Spin effects in the fragmentation of transversely polarized and unpolarized quarks