Based on the high-angle annular dark-field scanning transmission electron microscopy and energy dispersive X-ray spectroscopy studies, we unravel the origin of spontaneous core shell AlGaAs nanowires grown by gold-assisted molecular beam epitaxy. Our AlGaAs nanowires have a cylindrical core and a tapered shell. The composition of the shell is close to nominal, while the aluminum content in the core is systematically smaller than nominal. After switching off the group III fluxes, the aluminum content in the droplet and in the topmost part of the nanowire rapidly tends to zero, while gallium remains there at a high percentage. We present a quantitative model to explain these findings. Lower aluminum composition in the core is attributed to its lower surface diffusivity, with the aluminum collection length of 250 nm against 780 nm for gallium at the substrate temperature 510 degrees C and under the nominal aluminum content of 0.2. These values decrease to 8 and 160 nm when the nominal aluminum content is raised to 0.6. On the other hand, aluminum leaves the droplet at least 100 times faster than gallium, with a typical bonding rate with arsenic on the order of 1000 nm/s.