The unexpected "0.7" plateau of conductance quantisation is usually observed for ballistic onedimensional devices. In this work we study a quasi-ballistic quantum wire, for which the disorder induced backscattering reduces the conductance quantisation steps. We find that the transmission probability resonances coexist with the anomalous plateau. The studies of these resonances as a function of the in-plane magnetic field and electron density point to the presence of spin polarisation at low carrier concentrations and constitute a method for the determination of the effective g-factor suitable for disordered quantum wires.PACS numbers: 73.63. Nm, 73.23.Ad, 72.25.Dc It is expected that quantum point contacts (QPC) and quantum wires (QW) will act as active components of future nano-electronic devices and circuits. Therefore, the renewed interest in transport and spin properties of one-dimensional (1D) systems recently takes place in the mesoscopic physics community. In those studies, special attention is directed towards the long standing problem of quantum transport -the so called "0.7 anomaly" [1] most often, but not exclusively, observed for devices fabricated on modulation doped GaAs/AlGaAs heterostructures. Usually, anomalous behavior is observed in transport data as a "kink" on the conductance G vs. the device width curve, occurring for the low carrier densities, when G ∼ 0.7 × 2e 2 /h, here −e is the electron charge and h is the Planck constant. The origin of this effect is currently under active debate since this anomaly seems to be an universal, but still unexplained feature of one-dimensional mesoscopic transport. Experimentally, the magnetic field dependence of the additional plateau is common for all studied systems -by applying a parallel in-plane field the 0.7 feature evolves gradually towards 0.5 × 2e 2 /h conductance step, when only one spinpolarised level is occupied [1,2,3,4,5,6]. Therefore, it has been suggested that such an anomalous plateau is due to spontaneous spin polarisation of one-dimensional electron liquid, caused by exchange interactions among carriers in the constricted geometry of the device [2,7]. If it is so, the 1D systems may be used as an efficient spin filter with possible practical applications. This point of * Also at Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, Hoża 69, PL 00-681 Warszawa, Poland; ERATO Semiconductor Spintronics Project, Japan Science Technology Agency, 1-18 Kitamemachi, Aoba-ku Sendai, 980-0023, Japan † Also at ERATO Semiconductor Spintronics Project, Japan Science and Technology Agency, 1-18 Kitamemachi, Aoba-ku Sendai, 980-0023, Japan view is supported by magnetic focusing data obtained for the p-type device, which reveal the static spin polarisation of holes transmitted through the constriction [8].Furthermore, recent shot-noise measurements carried out for n-type QPC [9] show that distinct transport channels exist at G < 2e 2 /h = G 0 , presumably related to spin, exhibiting quite different transmission probabilities.Many experiments, howeve...