[sql-server-2008] T-SQL substring - separating first and last name

validate last name is blank

SELECT  
person.fullName,
(CASE WHEN 0 = CHARINDEX(' ', person.fullName) 
    then  person.fullName 
    ELSE SUBSTRING(person.fullName, 1, CHARINDEX(' ', person.fullName)) end) as first_name,  
(CASE WHEN 0 = CHARINDEX(' ', person.fullName) 
    THEN ''  
    ELSE SUBSTRING(person.fullName,CHARINDEX(' ', person.fullName), LEN(person.fullName) )end) last_name

FROM person