  We calculate the electronic structure of AA'AA'...-stacked alternating twist
N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk
alternating twist (AT) graphite systems where the lattice relaxations are
modeled by means of molecular dynamics simulations. We show that the symmetric
AA'AA'... stacking is energetically preferred among all interlayer sliding
geometries for progressively added layers up to N=6. Lattice relaxations
enhance electron-hole asymmetry, and reduce the magic angles with respect to
calculations with fixed tunneling strengths that we quantify from few layers to
bulk AT-graphite. Without a perpendicular electric field, the largest magic
angle flat-band states locate around the middle following the largest
eigenvalue eigenstate in a 1D-chain model of layers, while the density
redistributes to outer layers for smaller magic twist angles corresponding to
higher order effective bilayers in the 1D chain. A perpendicular electric field
decouples the electronic structure into $N$ Dirac bands with renormalized Fermi
velocities with distinct even-odd band splitting behaviors, showing a gap for
N=4 while for odd layers a Dirac cone remains between the flat band gaps. The
magic angle error tolerance estimated from density of states maxima expand
progressively from $0.05^{\circ}$ in t2G to up to $0.2^{\circ}$ in AT-graphite,
hence allowing a greater flexibility in multilayers. Decoupling of tNG into t2G
with different interlayer tunneling proportional to the eigenvalues of a 1D
layers chain allows to map tNG-multilayers bands onto those of periodic bulk
AT-graphite's at different $k_z$ values. We also obtain the Landau level
density of states in the quantum Hall regime for magnetic fields of up to 50~T
and confirm the presence of nearly flat bands around which we can develop
suppressed density of states gap regions by applying an electric field in N > 3
systems.
