We evaluate the topological character of TaAs through a detailed study of the angular, magnetic-field and temperature dependence of its magnetoresistivity and Hall-effect(s), and of its bulk electronic structure through quantum oscillatory phenomena. At low temperatures, and for fields perpendicular to the electrical current, we extract an extremely large Hall angle $Theta_H$ at higher fields, that is $Theta_H sim 82.5^{circ}$, implying a very pronounced Hall signal superimposed into its magnetoresistivity. For magnetic fields and electrical currents perpendicular to the emph{c}-axis we observe a very pronounced planar Hall-effect, when the magnetic field is rotated within the basal plane. This effect is observed even at higher temperatures, i.e. as high as $T = 100$ K, and predicted recently to result from the chiral anomaly among Weyl points. Superimposed onto this planar Hall, which is an even function of the field, we observe an anomalous planar Hall-signal akin to the one reported for that is an odd function of the field. Below 100 K, negative longitudinal magnetoresistivity (LMR), initially ascribed to the chiral anomaly and subsequently to current inhomogeneities, is observed in samples having different geometries and contact configurations, once the large Hall signal is subtracted. Our measurements reveal a phase transition upon approaching the quantum limit that leads to the reconstruction of the FS and to the concomitant suppression of the negative LMR indicating that it is intrinsically associated with the Weyl dispersion at the Fermi level. For fields along the emph{a}-axis it also leads to a pronounced hysteresis pointing to a field-induced electronic phase-transition. This collection of unconventional tranport observations points to the prominent role played by the axial anomaly among Weyl nodes.
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