  We present a global analysis of the observed Z_c, Z_cs and future Z_css-like
spectra using the inverse Laplace transform (LSR) version of QCD spectral sum
rules (QSSR) within stability criteria. Integrated compact QCD expressions of
the LO spectral functions up to dimension-six condensates are given.
Next-to-Leading Order (NLO) factorized perturbative contributions are included.
We re-emphasize the importance to include PT radiative corrections (though
numerically small) for heavy quark sum rules in order to justify the (ad hoc)
definition and value of the heavy quark mass used frequently at LO in the
literature. We also demonstrate that, contrary to a na\"ive qualitative 1/N_c
counting, the two-meson scattering contributions to the four-quark spectral
functions are numerically negligible confirming the reliability of the LSR
predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and
Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973)
tetramoles (superposition of quasi-degenerated molecules and tetraquark states
having the same quantum numbers and with almost equal couplings to the
currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1
molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be
likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a
radial excitation of the Z_c(3900) weakly coupled to the current, while all
strongly coupled ones are in the region (5634-6527) MeV. The double strange
tetramole state T_css which one may identify with the future Z_css is predicted
to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings
of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs=
(73- 91) MeV.
