While it is a given that Trowa admired Heero, I think it is more than that. No, I'm not falling into the realms of "shipping". There is already a separate area on this site for that. Let us go back into Trowa's history for a moment. In the television series, Colonel Une determined Trowa was "the perfect pilot". In Blind Target, Ralph Kurt saw No-name to be "the perfect soldier". All his life, Trowa had managed to perform his best and his elders all took note of this. All this time he is a young boy. Alone enough as it is, this "perfection" has set him apart from others. Possibly it is part of why he never grew attached enough to the Mercenary Corp. that raised him. They might have unknowingly set him apart from them not just by age difference, but because of his superiority at fighting.
On this train of thought, No-name showed seeming concern for the Captain. As No-name and as Trowa Barton, he has always respected those he considers his superiors. Like with his old Captain in Episode Zero, he even gives certain hints of actual admiration and respect for Une while undercover as an OZ officer. Trowa is capable of leading as he is used to working by himself, but the moment he discovers a person he considers an ally as well as superior to him, he will automatically follow.
This habit of his is displayed in his tendency to rise only so high up the ranks in anything he does. He was always part of mercenary units where the only real superior in terms of authority is the captain. As a mechanic to Heavy Arms, he never made himself stand out to become an assistant to a lead mechanic or even to the head mechanic. At the circus he does enough to stand out, but not enough to outshine the stars.
Now, consider when all five Gundam Pilots met at New Edwards and Wu Fei called the rest of them out on their folly. After that, Trowa immediately followed Wu Fei to assist him in going after Treize Khushrenada, but not to face Treize together. Instead he went to fight off any outside interference to allow Wu Fei to take on Treize one-on-one.
Unfortunately Wu Fei lost and Trowa understood his situation. Though he had taken Wu Fei in to the circus to recuperate, he knew Wu Fei was not superior to him, but was indeed an excellent soldier. He in turn had no problem letting Wu Fei leave.
Now let us return to Heero. Trowa also took in Heero after the 01 pilot was down. Though in this case, he "succeeded" in the mission given to him. When Heero awoke, Trowa looked to him for guidance. Thus he obviously sees Heero as a soldier that is superior to him and thus worthy of following. Which, of course leads to his own attempt to self-destruct, but also take out an OZ base like the original mission would have dictated.
Many consider Heero and Trowa to be suicidal, but I do not see that as the case. While both seem to hold their lives with little worth, they are not out to seek their deaths. If they had been the type, they could have ended their own lives plenty of times before. Thus, I do not believe Trowa's self-destruction attempt was out of suicidal tendencies. Like Heero, he is simply willing to die for what he believes in.
Simply put, Trowa considered Heero to be free because in being considered dead he no longer was a soldier with his hands tied. He was no longer a Gundam Pilot as he had no longer had a Gundam to pilot. Trowa and the other three remaining Gundam Pilots however were wandering soldiers without leave. They were at a stalemate and none of the Gundam Pilots are the sort to simply stand still for long. In turn, I believe that Trowa followed Heero's example because not only did he consider Heero above him as a soldier, he wanted to leave the limbo he was left in. If he saw his existence as a person to be worthless, what would he see his worth as a soldier who could only hide and protect his weapon?
With his attempt to self-destruct thwarted by Catherine's intervention, Trowa then decided to follow Heero afterwards rather than stay with the circus. (Would he have followed Wu Fei afterwards had the Chinese pilot succeeded in assassinating Treize to gain a sense of what to do afterward?) He likely did this to keep the circus safe by his absence and assuring there was no trace of association with him, but he also was still looking for a way to proceed forward. It seems he believed that by accompanying Heero, he would find his answer.
While Trowa sought his answer, he quietly observed Heero in his quest for redemption for the mistake he made at New Edwards. Everything he witnessed sealed his belief that the other boy was "the perfect soldier". All his life Trowa was known as "the perfect soldier". Now, for the first time ever, he has encountered a person he can consider being that title and it is a boy who is around his age at that.
If one recalls Episode Zero, there is only one other person he has ever considered to be like him. As No-name he had thought Midii Une was the same as him. He had been sure of it. In the end he had been mistaken. Now, a handful of years later he finally meets someone who really is like him. He found a kindred spirit in Heero Yuy.
Admittedly, Trowa's admiration and view of Heero as "the perfect pilot" may have changed a bit once the events in Antarctica took place. By changed, I do not mean he saw Heero as less than perfect or as a soldier, but instead he understood that even a perfect soldier is still human and will have flaws. A soldier can remain efficient and tactical with his or her emotions running rampant. Emotions can be used as a strength and are not a weakness.
Heero Yuy's existence established that Trowa was not alone. He wasn't the only "inhuman" boy his Captain made him out to be. He wasn't the only "perfect soldier", as Ralph Kurt pegged him as. He wasnt the only "abnormal" person as OZ Lieutenant Nichol would consider him later on. He wasn't the only teenager to bear the title of "the perfect soldier". There was finally someone, who was even a boy around his age, that he could understand and could understand him in turn.