We construct some radially symmetric solutions of the constant k -equation on R n n R p , which blow up exactly at the submanifold R p R n . These are the basic models to the problem of nding complete metrics of constant k {curvature on a general subdomain of the sphere S n n p that blow up exactly at the singular set p and that are conformal to the canonical metric. More precisely, we look at the case k = 2 and 0