Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric $chi^{2}$ solitons is considered in the 2D system with the quadratic nonlinearity. The spontaneous conversion is driven by the parametric instability of the SH wave. The input in the form of the AW vortex is considered too. As a result, one, two, or three stable solitons emerge in a well-defined form, unlike the recently studied 1D setting, where the picture is obscured by radiation jets. Shares of the total power captured by the emerging solitons and conversion efficiency are found as functions of parameters of the AW input.
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