It does depend on the regional court to some degree, but many urban jurisdictions these days make a presumption of joint custody and look at the income disparit

It does depend on the regional court to some degree, but many urban jurisdictions these days make a presumption of joint custody and look at the income disparity to determine the child support and/or alimony formula. There's no sex-preference involved beyond what you bring to the case (did she stay at home for maternity leave? Did he take paternity leave? How did the parenting responsibilities split?) Canada in particular has some challenges around vagueness with "best interests of the child" as the main focus of separation and customary and access cases... but for 20 years now there is almost no reason two partners wouldn't get joint access/custody 50-50 if one of them wants it and has shown past interest in parenting + doesn't have evidence of violent/absuive conduct. You'd have to fight for it potentially, if your former partner wants sole custody, but that's a very high bar to prove. court is potential great cost, but you would probably settle to 50/50 beffore it went to trial once reality sinks with your ex.