What does "does not work" mean? Could you be a bit more specific. Why
not use cascading deletes on foreign keys for this? See the ON DELETE
CASCASE option in Books Online for details.

Your trigger will fail to delete all related rows if more than one row
is deleted from the Admissions table. Don't write triggers that way. To
do it in a trigger, try this:

CREATE TRIGGER tr_DeleteAdmissionRelatedInfo
ON tblAdmissions
FOR DELETE

AS

DELETE FROM tblASIFollowUp
WHERE EXISTS
(SELECT *
FROM Deleted
WHERE admissionid = tblASIFollowUp.admissionid)

.... etc

If you need more help, please post some code that will actually
reproduce the problem, including the CREATE, INSERT and DELETE
statements (simplified if possible please).
--
David Portas
SQL Server MVP
--