  First, we simplify the existing classification due to Kawakita and Yamamoto
of 3-dimensional divisorial contractions with centre a $cA_n$-singularity, also
called compound $A_n$ singularity. Next, we describe the global algebraic
divisorial contractions corresponding to a given local analytic equivalence
class of divisorial contractions with centre a point. Finally, we consider
divisorial contractions of discrepancy at least 2 to a fixed variety with
centre a $cA_n$-singularity. We show that if there exists one such divisorial
contraction, then there exist uncountably many such divisorial contractions.
