  Nakajima introduced a resolution of singularities of the Donaldson-Uhlenbeck
completion of the moduli space of based instantons over $S^4$. For $k\leq 4$,
we extend this result to $\mathbb P^2$ and compute, in the rank-stable limit,
the homotopy type of these spaces by showing that, in this limit, these
constructions yield universal bundles.
