Every legislative session in New York state, hospital executives trek to Albany and corral their legislators in an effort to get more money and better terms for their struggling facilities in New York City. Last March, one such hospital's executives were on the case, lobbying Assemblyman Anthony S. Seminerio. According to a federal criminal complaint, the hospital and an affiliated health care plan were paying Seminerio for his help: about $390,000 since 2000. Although the complaint against Seminerio does not reveal the name of the hospital or the two executives recorded talking to him, several hospital industry officials said that the hospital described in the complaint fit the profile of Jamaica Hospital Medical Center in Queens.