A recent data base from direct numerical simulation of a turbulent boundary layer up to Reθ = 4300 [Schlatter & Örlü, J. Fluid Mech. 659, 2010] has been analysed in an effort to educe the dominant flow structures populating the near-wall region. In particular, the question of whether hairpin vortices are indeed observable as a dominant building block of near-wall turbulence is addressed. It is shown that during the initial phase, dominanted by the specific laminar-turbulent transition induced via the tripping mechanism, hairpin vortices are very numerous, and can certainly be considered as the dominant structure. This is in agreement with previous experiments and low Reynolds number simulations such as Wu & Moin [J. Fluid Mech. 630, 2009]. At sufficient distance from transition, the flow is dominated by a staggered array of quasi-streamwise vortices which is the same situation as in previous channel flows. It turns out that even quantitatively, no major differences between boundary layers and channels can be detected; structures are about 200 viscous units in length, and inclined by about 9 degrees [Jeong et al., J. Fluid Mech. 332, 1997]. The present results clearly show that the regeneration process of turbulence does not involve the generation of (symmetric) hairpin vortices, and that their dominant appearance as instantaneous flow structures in the outer boundary-layer region is at least very unlikely.