This paper investigates the laminar flow inside a T-mixer composed of three pipes with a circular cross section. The flow enters the mixer symmetrically from the two aligned pipes and leaves the device from the third pipe. In similar devices, but involving rectangular channels instead of pipes, an important regime for mixing has been identified, denoted as engulfment. Despite the symmetries of the flow and of the geometry, engulfment is an asymmetric steady regime, which is observed above a critical value (Re-c) of the flow Reynolds number. Conversely, for Reynolds numbers lower than Re-c, the flow regime is steady and symmetric, and it is usually denoted as the vortex regime. In this paper, both the vortex and the engulfment regimes are identified for the considered geometry, and they are characterized in detail by dedicated direct numerical simulations (DNSs). Despite an apparent similitude with the behavior of T-mixers employing rectangular channels, which are the most investigated T-mixers in the literature, substantial differences are observed and highlighted here concerning both regimes, i.e., the vortex and the engulfment ones, and concerning transition between the two. Global stability analysis is finally used in synergy with DNS to investigate the onset of the engulfment regime, which is shown to be related to a symmetry-breaking bifurcation of the vortex regime.