On their way home the 3 friends felt someone following them, they all looked at each other and nodded, splitting off and increasing their speed. All Might didn't expect this but he decided to increase his speed as well since he only has a couple of minutes in his bulk form.
Rushing towards where the green haired quirkless kid went off to, he arrived by landing right in front of him while saying.
"DON'T WORRY FOR I AM HERE!!" All Might yelled while doing is signerter pose. Izuku screamed because he didn't expect the pursuer to be All Might and especially for him to land right in front of him. Calming down, Izuku looked at All Might with a confused face.
"Why were you following me home? Oh, and don't worry I caught the villain that escaped earlier." Asked Izuku.
"I know, I saw you take care of the villain with your friends. It moved me that even though you don't have a quirk you didn't even hesitate in saving your friend. Not only that, you were able to figure out the weakness of the villain in such a short amount of time." All Might said in an impressed tone.
"As for why I followed you, I know that I said that you will never be a hero and you told me that you will prove me wrong. Well you did exactly that young man, and for that I came here to ask if you want to be my successor." All Might said in a serious tone.
"What do you mea--?!" Before Izuku could finish what he was going to say, All Might exploded a white cloud of dust around him and what came out was a skinny, weak old man.
"Wha- where did All Might go?" Izuku was super confused one minute he was talking to his idol and the next minute he just disappeared and this old man appeared. Looking more closely at the old man he realized that he and All Might had similar traits. Then it hit him.
"WAIT YOU'RE ALL MIGHT!!" Izuku's whole world just came crumbling, the all powerful All Might is actually this weak old man. Calming down, Izuku asked.
"What do you mean by me becoming your successor?" Shocked that the kid in front of him just went through so many emotions at once. All Might himself had to recollect his thoughts. All Might then tells Izuku everything about [One for All] and [All for One].
"If you decide to accept, all my burdens become yours and vice versa. Will you accept the burden?" All Might asked in a grave tone. Thinking about it for a while, Izuku nodded his head.
"Yes, I will be your successor." Izuku said with determination in his eyes and when he said that Axel and Katsuki jumped out of a bush that they were hiding in and yelled.
"CONGRATULATIONS, YOU FINALLY HAVE YOUR OWN QUIRK." The 2 boys couldn't help but smile brightly and run and grab Izuku in a big bear hug. The 2 boys were worried about Izuku since he wanted to be a hero with no quirk but they were going to try their best to help with his dreams anyways. Plague just shook his head at the idiocy of the boys.
Now that Izuku has a quirk, the 2 boys felt like a huge weight got taken off of their chest. While this was happening All Might stumbled he couldn't believe that he was spied on without him knowing.
"H-how much did you two hear?" All might said worriedly
"All of it." Said the boys simultaneously.
"Don't worry we won't say anything especially since it involves our friend now." Axel said with a bright smile. Sighing, All Might just had to accept the fact there were more people that know his quirk.
"Well since you all know my secret there is no use in lying about it. So before I give you my quirk you need to make sure you are physically capable or you will explode and die. Seeing you have some muscle I am going to need to test how much you are capable of lifting before I decide what to do next. But that can wait until tomorrow, meet me at Takoba Municipal Beach Park at 5 am, there we will test your strength." All Might said before leaving.
The 3 boys decided to celebrate with their family about Izuku getting a new quirk. They told their parents that after working out for so long Izuku eventually awakened his quirk which was a strength enhancing quirk. Now the three boys were excited that it will be a sure thing that all 3 will be admitted into UA highschool.
[Time skip]
10 months have passed since the first day of training with All Might. Izuku couldn't inherit the quirk at first but he wasn't that far off so it only took a couple of months for him to be ready. It only took 2 out of the 10 months for Izuku to inherit the quirk but he still increased his physical strength so he would have an easier time in controlling the quirk.
Apparently the stronger your physical base form is the more power you can use without hurting your body when you first try to control it. This is only part of it, eventually your base form only contributes little in the long run as you can tell by All Might's appearance but it is extremely helpful in the beginning.
We also learned that All Might is a horrible teacher, so we all had to come up with ways to find out how Izuku can control his power. And when I say all of us I mean mainly Izuku, that kid is way too smart when it comes to quirks.
Izuku found out how to properly control his quirk in the 3rd month during his training. So the next 7 months Izuku trained in his control of [One for All] and increased his original strength. Me and Katsuki weren't just sitting around either, we were also training our quirks and physical bodies at the same time.