Consider a Poisson process in R^d . Now start growing balloons at speed 1 from each point in this process, and if two balloons collide, 'pop' them (and remove the points in the Poisson process as well) Is the origin going to be visited infinitely many times by a balloon? What if we change R^d to the hyperbolic plane? We answer these questions demonstrating contrasting behaviour in these two cases. Bounding the density of a well separated factor of iid process on a tree comes up in the hyperbolic case, which is of independent interest. Joint work with Omer Angel, Thomas Budzinsky and Yinon Spinka sign up at https://sites.cns.utexas.edu/utgd/utgd-online-seminar for the zoom link