Jim Donegan, 43, was shot as he waited to collect his 13-year-old son from St Mary's Christian Brothers' Grammar School in west Belfast in December last year.
Launching a renewed appeal for information on the first anniversary of his "chilling murder", the Police Service of Northern Ireland (PSNI) said it believed two "violent groupings" were behind it - the Irish National Liberation Army (INLA) and the Oglaigh na hEireann (ONH).
Senior investigating officer Detective Chief Inspector Peter Montgomery said: "My investigation into the callous execution of Jim Donegan continues to progress and I have already publicly stated that a republican element is a main line of enquiry, specifically the INLA.
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"My enquiries now lead me to believe that ONH was also involved.
"I am confident that the answer to finding those involved in Jim's murder lies within the community and I am appealing to people living in the area around Clonelly Avenue - where the gunman emerged from before walking along the Glen Road to carry out the assassination - to cast their minds back to this day last year.
"You may think something you saw was insignificant but it may be the final piece of the jigsaw needed."
The force said that Mr Donegan was murdered as he sat in his red Porsche Panamera in Glen Road in West Belfast, waiting to pick up his teenage son.
The "cold blooded execution" was carried out by a lone gunman in front of hundreds of innocent school children and their parents, it added.
DCI Montgomery said the gunman was believed to have emerged from Clonelly Avenue into Glen Road at around 3.10pm, walked past numerous children, crossed the road at the pedestrian crossing, walked up to Mr Donegan's car then fired his weapon eight times before fleeing.
He added: "I know from talking to witnesses that people were aware of someone wearing a bright fluorescent jacket and that recollections are focused on this but I need people to try and remember if they saw the face of the person wearing it or anything unusual or distinct.
"He was wearing a high-vis hip length yellow jacket with security on the back, dark bottoms with a grey coloured hat or hood and carrying a dark bag over his shoulder which I believe contained the gun.
"I also believe the same man tried to murder Jim five days earlier in circumstances that would appear to be the carbon copy of the actual murder.
"Someone somewhere knows where he went after the murder, or may have helped him to escape out of the area unseen."
During the course of its investigation, the PSNI has seized 607 evidential exhibits, taken 213 statements, made 13 arrests, conducted 12 searches and seized and viewed 342 hours of CCTV, the PSNI said.
DCI Montgomery said the gunman may be late 30s to early 40s, approximately 5ft 8ins and may walk with a limp or may have an existing medical condition that impacts on his walking style.
He said Mr Donegan's family deserved answers and the community deserved to see the "dangerous" gunman sent to prison.
He added: "Jim was a husband, a brother, a father to two sons and a stepfather and this will be the second Christmas they will face without him.
"They deserve to have answers and this community deserves to have this dangerous man sent to prison for this callous murder.
"He thought nothing of firing indiscriminately up to eight times in an area crowded with young children and their parents at school pick up. Any one of those bullets could have gone astray and killed a child.
"And he didn't care that mums, dads, grandparents, young siblings and people in the community also saw the brutal slaying."
Witnesses should call the police on 101.