When you file a joint tax return with your spouse, you are essentially filing as a single unit - one taxpayer.
There isn't any way to divide up who pays what as you become "jointly and severally liable" for all items on the joint tax return. This means if one of you doesn't pay a tax liability the other is liable for the debt in its entirety, not only half or a pro rata share.
If one of you has a nontax debt that is being offset by a refund due, you can then apply for some separate accounting in some cases. This is done via the "Injured Spouse" form. If this is the case for your return you can learn more about that here.
For your W-4P, if you fill them out similarly you should have withholding that is roughly equivalent to your "share", though.
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