In general, for dioecious species, a large portion of the genome passed from parents to offspring of both sexes - in mammals the X-chromosomes and autosomes are passed from a mother to both daughters and sons, and autosomes from the father to both sons and daughters. Only the small amount of genes present in the Y-chromosome and mitochondria are inherited solely within one sex.
Is there any species (not just mammals) where most, or even all, of the genome is inherited in a sex-specific trajectory? What is the most sex-limited genome known to researchers?