What happened to the stones of the Beit Hamikdash in Jerusalem when it was destroyed?

There are various legends connected with them.

In the Talmud there is a mention of a synagogue in the Babylonian community of Nehardoa whose foundation was formed from stones of the Beit Hamikdash that the Jews took along with them when they went into exile.

This took place in regard to the first Beit Hamikdash. In regard to the destruction of the second one there is a legend that Heaven scattered those stones all over the world and wherever one of them landed a synagogue was eventually built on that site.