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ABSTRACT We present the first statistical analysis of kinematically resolved, spatially extended $$\rm Ly\alpha$$ emission around z = 2–3 galaxies in the Keck Baryonic Structure Survey (KBSS) using the Keck Cosmic Web Imager (KCWI). Our sample of 59 star-forming galaxies (zmed = 2.29) comprises the subset with typical KCWI integration times of ∼5 h and with existing imaging data from the Hubble Space Telescope and/or adaptive optics-assisted integral field spectroscopy. The high-resolution images were used to evaluate the azimuthal dependence of the diffuse $$\rm Ly\alpha$$ emission with respect to the stellar continuum within projected galactocentric distances of ≲30 proper kpc. We introduce cylindrically projected 2D spectra (CP2D) that map the averaged $$\rm Ly\alpha$$ spectral profile over a specified range of azimuthal angle, as a function of impact parameter around galaxies. The averaged CP2D spectrum of all galaxies shows clear signatures of $$\rm Ly\alpha$$ resonant scattering by outflowing gas. We stacked the CP2D spectra of individual galaxies over ranges of azimuthal angle with respect to their major axes. The extended $$\rm Ly\alpha$$ emission along the galaxy principal axes is statistically indistinguishable, with residual asymmetry of ≤2 per cent (∼2σ) of the integrated $$\rm Ly\alpha$$ emission. The symmetry implies that the $$\rm Ly\alpha$$ scattering medium is dominated by outflows in all directions within 30 kpc. Meanwhile, we find that the blueshifted component of $$\rm Ly\alpha$$ emission is marginally stronger along galaxy minor axes for galaxies with relatively weak $$\rm Ly\alpha$$ emission. We speculate that this weak directional dependence of $$\rm Ly\alpha$$ emission becomes discernible only when the $$\rm Ly\alpha$$ escape fraction is low. These discoveries highlight the need for similar analyses in simulations with $$\rm Ly\alpha$$ radiative transfer modelling.