Who gets the deductions for the kid?
If you are the custodial parent, you get everything unless you have signed it away on an IRS form 8332. Forget what the divorce decree says, that does not govern with the IRS. The only thing that works is the form 8332 and whether the other spouse is willing to permanently give up the child. This affects the dependency exemption, child tax credit, education credits, student loan interests deduction, tuition deduction, child care, earned income tax credit and tax free dependent care benefits and your tax status. Custodial parents get to claim Head of Household tax status which provides for many tax benefits including much lower tax rates. So proper planning is to be the custodial parent, if possible. If that cannot be achieved, then you will need a properly executed form 8332 before you get your divorce and property settlement if you are smart. Otherwise get it as soon as you can.
If the custodial parent waives the right to claim the child to you on a proper form 8332, you then can take the dependency exemption, child tax credit, education credits, student loan interest and tuition. You still must file as single as the non-custodial parent, but you do get those tax deductions.
The custodial tax parent even if they have transferred the dependency exemption to the other spouse on a valid form 8332 still gets to claim the beneficial Head of Household tax status tax rates.
Have no faith in the divorce agreements, get signed form 8332 in place which need to be filed with each return.