[avar]

    > Keep fining them more and more money
    > until they stop anti-competitive practices?

I believe you're referring to the EU's fines against Google here. In that case that's pretty much the only weapon the EU has. They can ultimately deny Google market access to the EU, and argue that case at the WTO, or seize Google's assets in the EU, but they can't decide to split up a US-based legal entity.

[trhway]

Due to various double sandwiches there a lot of non US Googles with good assets to go after.

[tobias3]

The EU also cannot prevent Google from buying US startups, furthering they monopoly position. And US startups get more funding because they might be bought by Google.