Fairfax County police have sent more than 370 e-mails around the world to acquaintances of Fuad K. Taima, asking them to view a composite drawing of the man they believe may have killed Taima and his family inside their McLean home in May.

The e-mails, sent to addresses gleaned from Taima's home computer, ask recipients to look at the drawing on the Fairfax police Web page. Taima, 63, his wife, Dorothy M. Taima, 54, and their son, Leith, 16, were found shot to death in their Broyhill Street home May 28.

Homicide Detective Robert Murphy said yesterday that police had ruled out any domestic-related motive in the shootings and that with the help of the FBI, detectives continue to focus on Fuad Taima's business dealings.

On May 17, Taima returned from a business trip to Baghdad, where he had helped arrange a deal for Valmet Automation Inc. to provide monitoring equipment for an oil pipeline between Iraq and Turkey.

FBI Special Agent Brad Garrett said he had interviewed Valmet employees who were involved in the transaction and had spoken by phone to some individuals with possible knowledge of Taima's business dealings. But neither he nor Murphy has traveled out of the country on the case.

Taima was a frequent e-mail user, so detectives from the police computer forensics unit obtained Taima's electronic address book and sent 378 e-mails to Taima's correspondents Sept. 3. Garrett said that "over a dozen" responses had been received and that they had provided some information for investigators.

"Do we have the scope narrowed down greatly? No, but it's narrower than it was," Garrett said.

The e-mail informed recipients of the slayings and said a middle-aged white male, with black hair and brown eyes, had visited the Taimas shortly before the slayings. The message provided a link to the Fairfax police Web page (www.co.fairfax.va.us/ps/police/murder.htm) for recipients to view the composite drawing of the suspect. Anyone with information was asked to phone or e-mail Garrett or Murphy.

"It's the first time we've taken this step [e-mail solicitation] in Fairfax County," said Detective Daniel L. Farrell, of the computer forensics unit.

Farrell said investigators have started to sort through the hundreds of floppy disks found in the Taima home but have not examined the hard drives of Leith Taima's personal computer or Dorothy Taima's computer at work.

"My enthusiasm is tempered," Farrell said, "because I have a lot of data to look at, and we've done it before in other cases, and it often doesn't pan out."

He said some of the e-mail addresses drawn from Fuad Taima's computer were for people in Iraq, Iran, Jordan, Syria and assorted European countries. Detectives have said Taima used e-mail extensively to try to drum up contacts for his struggling business enterprises.

A witness who was in the Taimas' home May 26 provided police with the description used to create the composite drawing of the suspect. The witness told police that Dorothy and Leith Taima clearly knew the man. The witness left the house about 10:35 p.m., and police believe that Fuad Taima returned home minutes later. Neighbors recalled hearing numerous shots about 10:45 p.m., although nothing was reported to police until the bodies were found two days later.

Yesterday, police continued to withhold most details about the shooting.

"Logic would dictate [the shootings] were connected to Iraq" because Taima had just returned from there, Garrett said.

The best lead police have is still the man in the drawing, Garrett said. "We don't know if he's the shooter," he said, "but he's the last one seen in the house, so he's somebody we've got to talk to."