Does Adsense decide by the content surrounding it or the content of the whole page? What if the topics are different is different sections of the page (for example homepage of a blog)?

Depending on the content and relevancy of the content.

Nima AdSense will look at a lot of things. What they're trying to do is provide the most relevant ad to your visitor. They'll look at the text around the ad, the text on the page itself, and even your site beyond the single page.

How they determine what to count most I couldn't really say.

The ads will also depend on how many people are bidding on phrases within your topic. If you write a page about blue widgets and no one is bidding on anything in the content network related to blue widgets AdSense can't show a relevant ad.

You can use something called section targeting to help Google know which content you want them to ignore on your site. So if you have 10 posts on the home page of your blog you could turn the section targeting on and off so only the content of one post is used to determine ads.

I've tried section targeting myself a little, but never found it to give me better ads. I didn't really experiment with it a lot though, so you have better results than I did.