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In our previous work [PSSW], we showed that the Ricci flow on S^2 whoseinitial metric has conical singularities \sum_{j=1}^k \beta_j[p_j] converges toa constant curvature metric with conic singularities (in the stable andsemi-stable cases) or to a gradient shrinking soliton with conicalsingularities (in the unstable case). The purpose of this note is to show thatin the unstable case, that is, the case where \beta_k>\beta_k'=\s_{j<k}\beta_j,that the limiting metric is the unique shrinking soliton with cone singularity\beta_k[p_\infty]+\beta_k'[q_\infty]. This verifies the prediction made in[PSSW].

Convergence of the conical Ricci flow on S2 to a soliton