  The amplitude for hard exclusive pseudoscalar meson electroproduction off
nucleon (nuclear) targets is computed in QCD within the leading $\alpha_s \ln
{Q^2/\lambda_{QCD}^{2}}$ approximation. We show that the distribution of recoil
nucleons depends strongly on the angle between the momentum of the recoil
nucleon and the polarization vector of the target (or outgoing nucleon). This
dependence is especially sensitive to the spin flip skewed parton distribution
(SPD) $\widetilde E$. We argue also that the scaling for this spin asymmetry
sets in at lower Q^2 than that for the absolute cross section. Basing on the
chiral quark-soliton model of the nucleon we estimate quantitatively the spin
asymmetry. In the case of pi+ production this asymmetry is dominated at small t
by the contribution of the pion pole in the isovector SPD $\widetilde E$ as
required by PCAC. In the case of K0 production off a proton we find a large
enhancement of the cross section as compared to the case of pi0 production. For
the forward production of neutral pseudoscalar mesons off a deuteron target we
find the cross section should be zero for the zero deuteron helicity (along the
$\gamma^*D$ direction). We consider also cross sections of quasielastic
processes off nuclei including the feasibility to implant K+,rho-mesons into
nuclear volume.
