  We give an alternate proof to the following generalization of the
uniformization theorem by Bonk and Kleiner. Any linearly locally connected and
Ahlfors 2-regular closed metric surface is quasisymmetrically equivalent to a
model surface of the same topology. Moreover, we show that this is also true
for surfaces as above with non-empty boundary and that the corresponding map
can be chosen in a canonical way. Our proof is based on a local argument
involving the existence of quasisymmetric parametrizations for metric discs as
shown in in a paper of Lytchak and Wenger.
