Context : The enigmatic object HD 45166 is a qWR star in a binary system with an orbital period of 1.596 day , and presents a rich emission-line spectrum in addition to absorption lines from the companion star ( B7 V ) .
As the system inclination is very small ( i = 0.77 ^ { \circ } \pm 0.09 ^ { \circ } ) , HD 45166 is an ideal laboratory for wind-structure studies .

Aims : The goal of the present paper is to determine the fundamental stellar and wind parameters of the qWR star .

Methods : A radiative transfer model for the wind and photosphere of the qWR star was calculated using the non-LTE code CMFGEN .
The wind asymmetry was also analyzed using a recently-developed version of CMFGEN to compute the emerging spectrum in two-dimensional geometry .
The temporal-variance spectrum ( TVS ) was calculated for studying the line-profile variations .

Results : Abundances , stellar and wind parameters of the qWR star were obtained .
The qWR star has an effective temperature of \mathit { T } _ { eff } = 50000 \pm 2000 \mathrm { K } , a luminosity of \mathrm { log } ( L / \mathrm { L } _ { \odot } ) = 3.75 \pm 0.08 , and a corresponding photospheric radius of \mathit { R } _ { phot } = 1.00 \mathrm { R } _ { \odot } .
The star is helium-rich ( N ( H ) /N ( He ) = 2.0 ) , while the CNO abundances are anomalous when compared either to solar values , to planetary nebulae , or to WR stars .
The mass-loss rate is \dot { M } = 2.2 \times 10 ^ { -7 } \mathrm { M } _ { \odot } { yr } ^ { -1 } , and the wind terminal velocity is v _ { \infty } = 425 { km s ^ { -1 } } .
The comparison between the observed line profiles and models computed under different latitude-dependent wind densities strongly suggests the presence of an oblate wind density enhancement , with a density contrast of at least 8:1 from equator to pole .
If a high velocity polar wind is present ( \sim 1200 { km s ^ { -1 } } ) , the minimum density contrast is reduced to 4:1 .

Conclusions : The wind parameters determined are unusual when compared to O-type stars or to typical WR stars .
While for WR stars v _ { \infty } / v _ { esc } > 1.5 , in the case of HD 45166 it is much smaller ( v _ { \infty } / v _ { esc } = 0.32 ) .
In addition , the efficiency of momentum transfer is \eta = 0.74 , which is at least 4 times smaller than in a typical WR .
We find evidence for the presence of a wind compression zone , since the equatorial wind density is significantly larger when compared to the polar wind .
The TVS supports the presence of such a latitude-dependent wind and a variable absorption/scattering gas near the equator .