  We discuss conjectural scaling limits of discrete 2-dimensional aggregation
models conditioned on a semi-axis considered by Levine and Peres in
arXiv:0712.3378. These are certain problems about Hele-Show flows. We study
moment properties of their solutions, and solve some of them using conformal
mappings. In particular, we predict the exact formula for the
computer-generated shape on the left side of Fig. 4 in arXiv:0712.3378.
