I don't have a clue as to Tyrek's current whereabouts... nor the location of his remains if he's dead. We've discussed the possibility of him actually being Aegon, Rhaegar's son, in
Tyrek Lannister as Aegon. I think we've discussed him being captive under Casterly Rock.
We do know that the mob did what they wanted with members of the royal entourage who could not gain the safety of the Red Keep. Lollys was gang raped. Aron Santagar, Preston Greenfield, and the High Septon were murdered.
What value does Tyrek posess?
Tyrek was Lord Hayford. He was married to Ermasande Hayford, an infant, in order for the Lannisters to gain her lands.
While Tommen is king, Jaime is in the KG, and Tyrion is under a death sentence, Tyrek is fifth in line to inherit Casterly Rock behind Cersei, Kevan, Lancel, and Martyn.
Or mayhaps he learned certain information while serving as Robert's squire/page. Mayhaps Tyrek knew about Cersei's infidelity. Mayhaps he knew of Jaime's fathering Joffrey, Myrcella, and Tommen. Mayhaps he knew of Lancel's liasons with Cersei. Mayhaps he stumbled upon some plot or treasonous court intrigue?
Who would benefit by kidnapping him?
Who needs to cover up their indiscretions? Cersei. In ACOK, Tyrion wonders if Cersei will kill Lancel to keep her secret... therefore, I'd guess that Cersei would not balk at removing Tyrek either.
Who would need to keep their plots secret? Tyrion, Pycelle, Varys and Baelish. But since we have at least ten Tyrion chapters after Tyrek's disappearance without even a whiff of Tyrion's involvement, I'd say Tyrion had nothing to do with Tyrek.
Pycelle was Tyrion's captive in the dungeons at the time... so I'd rule Pycelle out.
Now Baelish has secreted at least one teenager out of King's Landing... Sansa. Mayhaps he has Tyrek tucked away somewhere. But Baelish was on his way to the Tyrells to secure their alliance. He was not in KL, though he could have hired someone to instigate the riot and kidnap Tyrek. Remember that Sansa was grabbed and only Sandor's aggression saved her? Maybe he also wanted to kidnap Sansa at that time. If this is the case, then maybe we should look for Tyrek in the Vale.
This is scary, but mayhaps Tyrek is being secretly mentored by Lyn Corbray.
Varys may have been involved in baby Aegon's switch and in the flight of Viserys and Daenerys... and we know he uses children (from his conversation with Illyrion Mopatis in the dungeons)... Remember that Shae was a teenager... It seems that Varys is accomplished at moving children and teenagers around unseen by the public. Also, Varys was conspicuously not in the royal party that saw Mycella off. More curiously, later that night Bronn suggests to Tyrion and Varys that they could murder Joffrey and rule through Tommen. Did Varys plan the destruction of Joffrey and Cersei at the hands of the mob? Was he planning on setting Tommen on the throne?
It seems to me that Tyrek is only a year or two older than Joffrey... and Joffrey was tall for his age. Was someone planning to murder Joffrey and put Tyrek in his place? Say Tyrek was horribly disfigured, then mayhaps Varys could claim that Joffrey was seriously wounded in the mob attack. Of course this is far fetched, but I'm just guessing today.
I don't have any answers, just wild ideas.