Some of the Puella Magi seem to have magical powers related to the wishes that they made. Sayaka has regeneration abilities, and she wished to heal someone. Homura has time manipulation abilities, and she wished to go back in time.
But other magical girls, like Mami and Kyouko, don't appear to have powers related to their respective wishes.
So, is there a connection, or is it only a coincidence for Sayaka and Homura? If it's the former, how do Mami and Kouko's wishes relate to their powers?
From an interview in the July 2011 issue of Megami, as translated on the Puella Magi Wiki:
There's a few place in the script that I'd like to touch on, first about Mami and Kyoko. How is their "wish" connected to their powers when they became magical girls? In Mami's case, her wish "to connect to life" [editor's note: she wanted to live] gave her the power to "tie" and "combine" things together. That's why her power comes from the ribbon. By using the ribbon as a weapon, she can use that to produce guns that are useful in a battle. In ep3, Homura is stopped in her tracks by being tied up. That is her true magical power. She has the most experience so has a lot of different magical powers beyond those of her original powers.
And as for Kyouko (same source, different section):
Regarding Kyoko, it [her magic power] is really very special. Because she got her wish of "getting people to listen" while in fact it was something like charming or hallucination, she got the magic power related to those things. However, because she lost her family, she totally negated those power with her subconscious mind. As a result, she fought only with the magic power she learnt later. This is the "hidden setting" (ura-settei) for her, although we never got to tell it in the anime.
These answers were given by Urobuchi Gen, the writer for Madoka. Since he is explaining the relationship between Mami and Kyouko's wishes and their powers, I'd say it's safe to take this as official confirmation there is indeed an intentional relationship.
