I am looking for a company, group or division referred to as Air
Logics, they work with Doctors,Hmo groups and insurance companies
relating to asthmatic children. I heard them mentioned at Parkland
hospital in Dallas, Tx.

Hello tcb1935 and thank you for your question.

The company you are (almost certainly) looking for is called Airlogix

"AirLogix is the pioneer and leader in comprehensive respiratory
disease management services with over 300,000 patient lives managed.
We offer flexible, innovative solutions that meet the diverse needs of
managed care organizations including specialized care for chronic
respiratory diseases, improved quality of life, and reduced medical
costs."
http://www.airlogix.com/

Their contact information is:
"By telephone: (800) 293-0056
By email: WeCare@Airlogix.com
By fax: (214) 576-2049

Corporate office location:

AirLogix, Inc.
9461 LBJ Freeway
Suite 200
Dallas, TX 75243-4535"
http://www.airlogix.com/about_contact.htm

Thank you for your question, and if you neeed any clarification
regarding my answer, do not hesitate to ask.

Very best regards

THX1138
Search strategy included:
"air logics" and then lateral thinking on the spelling options!
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&safe=off&as_qdr=all&q=+%22air+logics%22