  In this work we deal with a scalar spectral mixed boundary value problem in a
spacial junction of thin rods and a plate. Constructing asymptotics of the
eigenvalues, we employ two equipollent asymptotic models posed on the skeleton
of the junction, that is, a hybrid domain. We, first, use the technique of
self-adjoint extensions and, second, we impose algebraic conditions at the
junction points in order to compile a problem in a function space with detached
asymptotics. The latter problem is involved into a symmetric generalized Green
formula and, therefore, admits the variational formulation. In comparison with
a primordial asymptotic procedure, these two models provide much better
proximity of the spectra of the problems in the spacial junction and in its
skeleton. However, they exhibit the negative spectrum of finite multiplicity
and for these "parasitic" eigenvalues we derive asymptotic formulas to
demonstrate that they do not belong to the service area of the developed
asymptotic models.
