From the NY Times:
It is the worst-kept secret in City Hall. Michael R. Bloomberg has told almost everyone who asks — but only privately, so far — that he hopes the City Council speaker, Christine C. Quinn, will succeed him as mayor in 2013.
While Mr. Bloomberg brings unprecedented personal resources to his political agenda, few other New York City mayors have succeeded in anointing a successor.
Mr. Bloomberg, in fact, was the only mayoral candidate in recent memory for whom an endorsement by the incumbent proved instrumental, even if it was a begrudging, last-minute nudge from Rudolph W. Giuliani.
Mr. Bloomberg, an independent, has refrained from specifying an heir publicly, since he seems to prefer to keep Ms. Quinn, a Democrat, and other prospective candidates as compliant as possible in the two years remaining before the next mayoral election.