Courting support from labor unions and other potential supporters, the campaign of County Controller Mark Patrick Flaherty has been quietly circulating poll numbers, which show their candidate with a substantial lead among Democratic voters over Rich Fitzgerald, the county council president who is his rival for the nomination to succeed Dan Onorato as chief executive.

The survey of 403 Democrats deemed like to vote in the primary showed Mr. Flaherty ahead of Mr. Fitzgerald, 44 percent to 16 percent, with 40 percent undecided in a trial heat of their primary matchup.  The poll was conducted by the Democratic firm GarinHartYang of Washington D.C.

Mr. Fitzgerald dismissed the significance of the survey, taken almost ten months in advance of the May 17 primary.

“It occurred after he spent thousands running television ads;’’ Mr. Fitzgerald said. “He knew this race was coming and that was all about generating name recognition for fund-raising.’’

Mr. Flaherty’s year-end contribution financial report details extensive ad buys on the city’s three broadcast television stations, starting early last summer, for commercials in which the controller touted his prowess as a guardian of the accuracy of weights and measures in county commerce.

According to a January memo from the polling firm, the controller held a commensurate lead over Mr. Fitzgerald in name recognition as 68 percent of the Democratic voters recognized Mr. Flaherty while just 31 percent could identify Mr. Fitzgerald.

Mr. Fitzgerald insisted that the summer numbers would be meaningless by the time of the May 17 primary.  He predicted that he would, by then, hold such a dramatic lead in campaign funds that the name recognition and horse race numbers would be reversed.

The most recent campaign finance disclosures showed the two campaigns on relatively even footing in terms of cash on hand in January.  Mr. Fitzgerald maintained, however, that his contributions were now “pouring in the door,’’ after the news last month that Dan Onorato would not seek a third term.