This is joint work with Eyal Neuman and Jong Jun Lee, based an a question of Alexei Kuznetzov. We consider a stochastic flow in Euclidean space of dimension n, driven by a single Brownian motion. There is also a flow pointing away from the origin. We give a fairly sharp answer to the question of finding the critical drift which would allow the flow to hit 0 or not. In high-dimensional or infinite-dimensional situations, the usual tools for studying such questions break down.