  This work deals with the prompt pp-->pp3pi0 reaction where the 3pi0 do not
origin from the decay of narrow resonances like \eta(547), \omega(782),
\eta'(958). The reaction was measured for the proton beam momentum of 3.35GeV/c
with the WASA-at-COSY detector setup. The dynamics of the reaction is
investigated by Dalitz and Nyborg plots studies. The reaction is described by
the model assuming simultaneous excitation of two baryon resonances
\Delta(1232) and N*(1440) where resonances are identified by their unique
decays topology on the missing mass of two protons MMpp dependent Dalitz and
Nyborg plots. The ratio
R=\Gamma(N*(1440)->N\pi\pi)/\Gamma(N*(1440)->\Delta(1232)\pi->N\pi\pi)= 0.039
+- 0.011(stat.) +- 0.008(sys.) is measured for the first time in a direct way.
It shows that the {N*(1440)->\Delta(1232)\pi->N\pi\pi} decay is a leading mode
of 3pi0 production. It is also shown that the MMpp is very sensitive to the
structure of the spectral line shape of the N*(1440) resonance as well as on
the interaction between the \Delta(1232) and N*(1440) resonances. The multipion
spectroscopy - a precision tool to directly access the properties of baryon
resonances is considered.
  The pp-->pp\eta(3pi0) reaction was also measured simultaneously. It is shown
that the {\eta} production mechanism via N*(1535) is 43.4 +- 0.8(stat.) +-
2.0(sys.) of the total production, for the {\eta} momentum in the CM system
q_\eta^CM=0.45-0.7GeV/c. First time momentum dependence of the {\eta} angular
distribution is seen, the strongest effect is observed for the
cos(\theta_\eta^CM) distribution.
