Millions of fathers who do not live with their children are evading legal child-support obligations, the Census Bureau reported yesterday.

The bureau said only half of the 4 million mothers in the nation who are legally entitled to child support from an absent father in 1983 received the full amount due.

For various reasons, nearly 4 million other women with children whose fathers were not at home did not even have child-support orders, according to the study.

The report underscores the reasons why Congress, believing that lack of child support from absent fathers is a major contributor to poverty and deprivation, passed bipartisan child-support legislation last year with strong backing from Health and Human Services Secretary Margaret M. Heckler.

The law seeks to force states to strengthen programs designed to find nonsupporting fathers and make them pay. A key feature of the legislation is the requirement that states create mechanisms for speedy automatic deduction of overdue child-support payments from a father's wages, normally without having to seek court backing again.

The survey found that, in 1983, 8.7 million women had children under 21 whose fathers were absent but only 4 million had legal child-support orders or voluntary agreements entitling them to child-support payments.

Of the remainder, 3.7 million had no child-support orders, in some cases because they had taken property settlements in lieu of child support and in others because they could not locate the father or establish paternity or believed that the father had no money.

The other 1 million had legal orders but were not due support for 1983 because the child had passed the eligibility age, the father had died or similar reasons.

Of the 4 million mothers with valid 1983 support orders, the bureau found that only 2,018,000, or 50.5 percent, received the full amount. Another 1,019,000, 25.5 percent, received partial payment, and 958,000, or 24 percent, received nothing.

Support payments due the 4 million totaled $10.1 billion but, because of underpayments and defaults, only $7.1 billion was received. If all payments had been made, about 80,000 fewer families would have been in poverty.

The bureau found that the average support payment received was $2,341 per mother and that well-educated and white women were more likely to obtain payment orders and collect than less well-educated and black and Hispanic women.

Two-thirds of white and college-educated women won support orders, but only 34 percent of black, 41 percent of Hispanic and 42 percent of mothers with fewer than 12 years of education did so.

The survey also measured receipt of alimony and found that, of 17.1 million women legally divorced or separated as of spring 1984, only 14 percent had been awarded alimony payments and that only one-third of those -- 791,000 -- were entitled to payments in 1983.