Former senator Adlai E. Stevenson III goes into the Illinois Democratic Central Committee's slate-making sessions this week virtually assured of the party's endorsement for governor.

Former governor Daniel Walker pulled out of the Democratic race yesterday, urging his supporters to work enthusiastically for Stevenson. By last week, Stevenson, who retired from the Senate last year, had lined up more than half the weighted vote he needs to get the party's backing in its committee hearings today in Springfield and Wednesday in Chicago.

Walker had hoped to get the support of Chicago Mayor Jane Byrne, but she stayed clear. Byrne has had several scraps with Stevenson over the years, and he is closely associated with her bitterest rival, Cook County State's Attorney Richard M. Daly.

Also, polls taken by the Byrne camp and by the Chicago newspapers showed Stevenson would make the strongest candidate against two-term Republican Gov. James R. Thompson.

"I said when I first announced my candidacy that I would not consider a primary fight, and I will not," Walker said after dropping out. Commenting on Walker's withdrawal, Stevenson said the former governor "has proven himself to be a man of his word."

Chicago attorney Alex R. Seith, who has run twice for the U.S. Senate, pulled out of the race about 10 days ago.