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We construct open sets of degenerate unfoldings of heterodimensional cyclesof any co-index $c>0$ and homoclinic tangencies of arbitrary codimension $c>0$.These sets are known to be the support of unexpected phenomena in families ofdiffeomorphisms, such as the Kolmogorov typical co-existence of infinitely manyattractors. As a prerequisite we also construct robust homoclinic tangencies oflarge codimension which cannot be inside a strong partially hyperbolic set.

Robust degenerate unfoldings of cycles and tangencies