  We extend {Schramm's cofat uniformization theorem} to domains satisfying
conditions involving {quasitripods}, i.e., quasisymmetric images of the
standard tripod. If the non-point complementary components of domain $\Omega
\subset \hat{\mathbb{C}}$ contain uniform quasitripods with large diameters and
satisfy a {packing condition}, then there exists a conformal map $f\colon\Omega
\to D$ onto a circle domain $D$. Moreover, $f$ preserves the classes of
point-components and non-point components. The packing condition is satisfied
if $\Omega$ is {cospread}, i.e., if the complementary components contain
uniform quasitripods in all scales.
