* A woman in Michigan goes on welfare when her ex-husband, who makes $50,000 a year, refuses to make his child-support payments.
* A woman in Maryland spends 19 years trying to extract the $5 per week per child owed by her former spouse, without success.
* A man from Virginia skips to four different states over several years in an effort to avoid paying child support.
''Child support is the last bill a man pays each month and the first one he stops when things get tough,'' says Bettianne Welch, a divorced mother from Virginia. Her complaint is legion across the country: Of the 7.1 million women who had children under 21 present in the home in 1978, says the Census Bureau in a study published last year, only three-fifths were awarded any kind of child support. Less than half of those received their full amount - an amount that averages $1,800 per year.
''When people hear about child support, they think you're talking about the extras - the new car, the summer vacation. But you're talking about survival: the rent, the food,'' says Ms. Welch, whose 1978 divorce put her in the growing ranks of single-parent families; between 1970 and 1979, their numbers rose by 80 percent in this country.
With sheer numbers - but little money or power - behind them, people like Ms. Welch have started organizing into small, grass-roots lobbies for better enforcement of child support.
With names like KINDER (Kids In Need Deserve Equal Rights) and FOCUS (For Our Children's Unpaid Support), perhaps a half-dozen such groups have formed in the last five years. They bring their horror tales to the courts, the media, and the state houses, hoping for tougher legislation - and heavier enforcement of the present laws.
Under a 1975 amendment to the Social Security Act, all custodial parents are entitled to federal help in obtaining court-ordered child support payments from the noncustodial parent. According to Michelle Jefferson of the Federal Office of Child Support Enforcement, this is how the system is supposed to work:
If one parent fails to make his payments, the other parent works - typically through the local welfare office - to obtain a court order requiring him to do so. Then the state child-support enforcement office goes looking for the man, using various resources to dig up his address.
If the state office can't find him, the man's name is sent to the federal Parent Locator, which claims a 70 percent success record of turning up addresses.
Assuming the address is accurate, the state enforcement office then attempts to contact the man and set up a schedule of payments, sending out notices if the payments fall in arrears. Once the payments have fallen too far behind (and this varies from state to state), the agency has an option of taking the man to court where, according to the state in which he is prosecuted, the judge may order his wages garnisheed, have his employer take out child support automatically with each paycheck, or send the offender to jail.
According to Ms. Welch and others, the system is subject to breakdown at every point. Elaine Fromm, secretary for the two-year-old Organization for the Enforcement of Child Support (OECS) in Maryland, gives her own case as a classic example.
Divorced while still pregnant with her fourth child, she was awarded support in the amount of $5 per week per child - an amount she claims she never collected. She went onto welfare with four children under the age of four years, and worked with probation officers and the legal aid bureau to obtain her support.
''But nothing was ever done - I'd get a form letter occasionally, saying how much he was in arrears. And the legal aid officer asked me why I cared - after all, I was on welfare.''
Those who apply for Aid to Families with Dependent Children (AFDC), like Ms. Fromm, sign over their rights to any child-support payments to the state, says Ms. Jefferson, unless the child support exceeds the amount of welfare granted to that family. In that case, the family is taken off welfare. Some 46,000 families were removed from the AFDC rolls this way in 1981.
Ms. Fromm's organization is lobbying for a bill that would require the State of Maryland to enforce the support obligations owed by absent parents to their children, locate absent parents, establish paternity, and establish support orders for all custodial parents - not just those whose incomes fall below 50 percent of the median for the state, as the law in Maryland now requires.
Maryland's seeming inequity is just one tiny ripple in a wavy legal landscape of state child support laws. Although all 50 states, the District of Columbia, and US territories had passed bills guaranteeing child support reciprocity by 1957, says Ms. Jefferson, the nature of that reciprocity varies widely from state to state.
''If a court in Michigan orders that a man's wages be garnisheed, and he's skipped to Texas, the court in Texas won't honor it because Texas law doesn't include garnisheeing. That doesn't preclude them from doing something else, however,'' she says.
Two bills now before Congress may sidestep this problem. One, introduced by Rep. Clarence Long (D) of Maryland at OECS's urging, would allow IRS tax refunds to be given to custodial parents for child support, if payments are overdue. A provision already exists for this step to be taken in the case of single parents on welfare; Representative Long's bill would extend it to those not on welfare.
Another, broader bill introduced this year by Rep. Shirley Chisholm (D) of New York asks for a study of the ''appropriate federal role in the enforcement of alimony, child support, and property settlement orders,'' to see if federal legislation would cure the state-by-state approach to enforcement.
''We need to reach the taxpayer,'' says Patricia Kelly of Michigan's KINDER. ''If they only knew how much of their money was being spent to suppport us - if they enforced child-support payments, I bet they could take 70 percent of these women off welfare.''