What determines sex in birds?
Sex Determination System

Birds have a ZW sex determination system meaning that males are the homogametic sex. Or yet, in other words, males have two Z chromosomes while females have one Z and one W chromosome. You might want to have a look at Do males of all sexual species have Y chromosomes? for a short review of the diversity of sex determination system.

Dosage compensation

In birds dosage compensation exist but appear quite different than in mammals (Mank and Ellegren, 2009; Mank et al., 2011; Uebening et al., 2015; Naurin et al. 2009)

Sex determining locus

The DMRT1 gene on the Z chromosome appears to be important for male sex determination by affecting the testicular marker, SOX9 however it might not be the whole story (Smith et al. 2009). It is possible that several loci are involved in determining sex in birds.