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We study the electronic structure and band topology of fully relaxed twistedmulti-layer graphene (TMLG). Isolated flat bands emerge in TMLG with the numberof layers [$M+N$ with $M$ the layer number of the bottom few-layer graphene(FLG)] up to 10 and with various stacking orders, and most of them are on thehole side. The touched bands of FLGs around the Fermi level are split by themoir\'{e} coupling through the electron-hole asymmetry in low-energy bands ofFLGs and by the vertical hopping between next-nearest layers. The fullstructural relaxation leads to global gaps that completely isolate a flat band.For TMLG with given $M$ and $N$, the highest magnitude of Chern numbers ($|C|$)of the separable flat bands reaches $M+N-1$ and can be hosted by certainisolated bands. The $|C|=9$ occurs in the isolated flat valence band of severalconfigurations with 10 layers. Such high $|C|$ originates from the lifting ofthe band-state degeneracy in the weak regime of moir\'{e} coupling or from thetopological phase transitions induced by the strong moir\'{e} coupling.Moreover, large orbital magnetic moments arise in isolated flat bands with high$|C|$ and depend on the structural configurations of TMLG.

Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene