Portable toilets have been located around the Holmdel High School athletic fields for as long as many people familiar with the space can remember.

"They're always here," said a man who was visiting with his wife as their children were practicing the long jump on the track Saturday.

The man, who declined to give his name, says his family's visit to the athletic complex aren't that frequent, but he remembers one thing -- the outdoor toilets have always been there.

So why then didn't the superintendent from the neighboring Kenilworth school district, Thomas Tramaglini, make use of them instead of allegedly defecating on the track? It's one of many questions left unanswered in this bizarre story that has captured international attention.

No one answered the door at Tramaglini's townhome in Aberdeen Saturday. Other than a terse "I have no comment" offered to a NJ.com reporter who approached him on Friday afternoon, Tramalglini has issued no formal statement about the accusations.

These three portable toilets are about 80 steps from the running track. (Allison Pries | NJ Advance Media for NJ.com)

Police arrested Tramaglini last Monday after surveillance cameras allegedly caught him in the act. During a hastily arranged Kenilworth Board of Education meeting on Saturday morning, the superintendent was placed on paid leave until June 30 for allegedly repeatedly using the open track as a place to relieve himself.

Thomas Tramaglini

In the absence of any public defense from the accused, theories have abounded, including the possibility that Tramaglini (who has competed in the New York City Marathon) might have suffered from a common affliction known as "runner's trots" -- a sudden and not entirely controllable need to void mid-run. But as many others have noted, if this was occurring on a regular basis, that would suggest intent.

"The fact that it's repeated means that it's intentional," clinical psychologist Edward Hollenbach told NJ.com on Friday. "The person is weaponizing the emotion of disgust and using it to upset people."

However, at least one mystery -- the question of whether there was a place Tramaglini might have properly relieved himself on or near the Holmdel High School running track -- would appear to be solved.

The red synthetic Holmdel running track is about 80 steps from a bank of three portable toilets -- one which is handicapped accessible and two regular size units.

All three were unlocked on Saturday afternoon.

Whether these portable toiliets are left unlocked around the clock or just during certain hours was not clear Saturday.

Calls and an email to Holmdel Board of Education President Vicky Flynn, who is also on the building and grounds committee, were not immediately returned.

Attempts to reach other board members, school officials and coaches were unsuccessful.

The few people at the complex on Saturday said they either didn't know about the alleged acts of Tramaglini case or they didn't want to talk about it.

Two men leaving the field said they didn't know anything about it.

A few steps later, one turned around and said, "That guy isn't the superintendent of this school, you know."

Allison Pries may be reached at apries@njadvancemedia.com. Follow her on Twitter @AllisonPries. Find NJ.com on Facebook.