  In this paper, we study punctured spheres in two dimensional ball quotient
compactifications $(X, D)$. For example, we show that smooth toroidal
compactifications of ball quotients cannot contain properly holomorphically
embedded $3$-punctured spheres. We also use totally geodesic punctured spheres
to prove ampleness of $K_X + \alpha D$ for $\alpha \in (\frac{1}{4}, 1)$,
giving a sharp version of a theorem of the first author with G. Di Cerbo.
Finally, we produce the first examples of bielliptic ball quotient
compactifications modeled on the Gaussian integers.
