In reply to ronholm :
Last question first...for all courts in my jurisdictions cases are randomly assigned by computer when you file pleadings. Specifically implemented because of "judge shopping."
Second...keep in mind there are 2 types of custody: legal and physical. Almost universally parties are granted joint legal custody; i.e., right to medical records, school records, etc. As far as physical custody, primary physical custody is often a matter of practical matters such as residence proximity to schools or respective parents work schedules, etc. Although it is changing in our society traditionally mothers tend to be primary caregivers, though that is obviously not always the case. Additionally, child's prfrence is often a consideration, especially if beyond age of 12. Childs preference is merely a consideration for judge, not controlling. Other considerations may include desire to keep siblings (and half siblings) together.
Joint physical custody does not come down to exact physical time together. But generally pretty close to 50/50.I've had unique cases where parents live close enough to each other that children, especially older ones, essentially float between two households.
One thing I encourage with parents is they are better served to come up with a system they can all live with rather than turn it over to 3 strangers in the form of a judge and 2 lawyers to come up with a plan no one can live with.
When the parties can't agree it becomes necessary for judge to make a decision. Forced joint custody usually doesn't work. In any event, all my judges give very liberal visitation to non primary custodians, like several weeks in summer, visitation beyond just two weekends per month, extended holiday visitation, etc.
Parental alienation is real and even if not overt can arise subconsciously. That being said, you are better served if you keep adult matters and issues between parents although frustration can get to you, avoid even inadvertent alienation. Kids who see conflict between their divorced parents invariably blame themselves .
Finally it is pretty clear from what I've observed as well as a number of studies that primary custodial parents have a more difficult time financially even considering child support awards. Seems to be a function of the non custodial parent taking attitude "well I'm paying what judge ordered so my financial obligation is met."