We use 25 simulated galaxies from the NIHAO project to define and characterize a variety of kinematic stellar structures: Thin and thick discs, large-scale single discs, classical and pseudobulges, spheroids, inner discs, and stellar haloes. These structures have masses, spins, shapes, and rotational support in good agreement with theoretical expectations and observational data. Above a dark matter halo mass of 2.5 × 1011Mθ, all galaxies have a classical bulge and 70 per cent have a thin and thick disc. The kinematic (thin) discs follow a power-law relation between angular momentum and stellarmass J= 3.4M1.26±0.06, in very good agreement with the prediction based on the empirical stellar-to-halo-mass relation in the same mass range, and show a strong correlation between maximum 'observed' rotation velocity and dark matter halo circular velocity vc = 6.4v0.64±0.04 max . Tracing back in time these structures' progenitors, we find all of them to lose a fraction 1 - fj of their maximum angular momentum. Thin discs are significantly better at retaining their high-redshift spins (fj ∼ 0.70) than thick ones (fj ∼ 0.40). Stellar haloes have their progenitor baryons assembled the latest (z1/2 ∼ 1.1) and over the longest time-scales (τ ∼ 6.2Gyr), and have the smallest fraction of stars born in situ (fin situ = 0.35 ± 0.14). All other structures have 1.5 ≲ z1/2 ≲ 3, τ = 4 ± 2Gyr, and fin situ ≳ 0.9.