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Yes. Annulment decree payments qualify as deductible alimony payments. They also would be considered taxable income to the recipient. They should be reported as alimony (adjustment or income) on IRS Form 1040 page 1.

Generally, the wording in the divorce or separation decree identifies the payments as Alimony or something other than Alimony, such as child support. Alimony is income to the recipient and an adjustment to income for the payer. Generally, for payments to be considered alimony, seven characteristics should be present. The payments are in cash or check. The payment must be paid under a divorce decree or separation instrument. The divorce decree or separation agreement cannot designate the payment as a payment which is not deductible by the payer or includable in gross income by the recipient. The recipient and the payer must not be members of the same household. The payments must not be treated as child support. The taxpayer and spouse may not file a joint return with each other. There must not be a liability to make any payment for any period after the death of the spouse.

For 2013:
The Tax between 0 and 8,925 = 10%,
between $8,925 and $36,250 the Tax = 870 plus 15% over 8,925,
between $36,250 and $87,850 the Tax = 4,868 plus 25% over 36,250,
between $87,850 and $183,250 the Tax = 17,443 plus 28% over 87,850,
between $183,250, and $398,350 the Tax = 43,843 plus 33% over 183,250,
between $398,350, and $400,000 the Tax = 43,843 plus 33% over 398,350 over $400,000 the Tax = 116,163.75 plus 39.6% over 400,000.
For 2012:
The Tax between 0 and 8,700 = 10%,
between $8,701 and $35,350 the Tax = 870 plus 15% over 8,700,
between $35,351 and $85,650 the Tax = 4,868 plus 25% over 35,350,
between $85,651 and $178,650 the Tax = 17,443 plus 28% over 85,650,
between $178,651, and $388,350 the Tax = 43,843 plus 33% over 178,650,
over $388,351 the Tax = 112,863 plus 35% over 388,350.

An Alimony trust is a formal trust arrangement where the beneficiary of the trust is the ex-spouse entitled to alimony payments.
The settler or person who contributes property to the trust is the ex-spouse obligated to make the alimony payments.
The taxpayer may establish a post death "testamentary" trust or a living "inter vivos" trust to provide for the alimony payments required by a divorce decree or an agreement between the parties.

There are many factors to clarify before you claim your child as a dependent. Generally a special rule favoring the custodial parent applies where divorced or separated parents together, provide more than half the child's support.
The custodial parent will meet the dependency support test even if she did not pay half the child's support.
The parents may arrange for the non-custodial parent to claim the child if IRS Form 8332 is signed by the custodial parent and supplied with the non-custodial parents tax return.
Form 8332 is a waiver of claiming the exemption and the exemption waiver can be used for that year only or for future years as well. Speak to your local CPA about the other criteria in claiming the child and about Form 8332.

A noncustodial parent does not lose the right to claim the child's medical expenses (health insurance, drs, dentists prescription drugs etc.) as an itemized deduction on IRS Schedule A (subject to the 10% or 7.5% AGI limitation)if both the custodial and noncustodial parent together provide more than half of the support of the child and either had custody for at least six months during the year.

Divorced parents are entitled to custody of their minor children after death of a parent who had sole custody unless a court order provides otherwise. In general, It must be proven that it is specific detriment to the child in order to remove a child from the custody of a surviving parent and place the child in the custody of a non-parent. The court makes decisions based on the best interests of the child. Because parents have superior rights to custody over all other non-parents, a different standard is used when making custody decisions between a parent and a non-parent. If a court awarded sole custody to one parent, this is not proving that it would be detrimental to the child for the other parent to have custody. Sometimes a court must choose between 2 good parents. A parent with sole custody does not have the right to give or "will" this custody to someone else. Any parent can nominate a guardian for their child in their will. If the other parent is unable or unwilling to take charge of the child after your death, the court must consider your guardianship petition. The court must still consider the child's "best interests" and may grant guardianship to a non-parent.

No. There is no minimum payment period. Recapture of alimony amounts may apply where payments decrease by more than $15,000 within the first three years of the divorce.

The deductible alimony payments made in the first year or second year may have to be recaptured as income in the third year where the alimony payments within the first 3 years decrease by more than $15,000. Payments made in the second after the separation year are recaptured if the payments exceed the payments in the third post separation year by more than $15,000. Payments made in the first after the separation year are recaptured as income if they exceed the "average" payments made in the second post separation year and the third post separation year by more than $15,000. The recaptured amount is reported on IRS Form 1040 on the line Alimony received with a notation Alimony recapture with the payee spouse’s social security number.

When both alimony and child support are made together in a monthly payment, it is presumed that child support is paid first.
If your husband did not pay the full amount in a month or many months, then you need to pick up as income the difference over the child support amount for that month as alimony and income on your tax return.
It is reported on IRS Form 1040, page 1.