The punishment was surprising, both for its size and where it was imposed. Italy’s competition watchdog recently fined Amazon €1.13 billion ($1.28 billion) for allegedly privileging sellers who use the company’s logistics services. Not long before, the Italian regulators leveled a series of multi-million euro fines last year against Apple, Google, and Facebook.

The message was clear: it’s not only Brussels that is cracking down on US Big Tech. It’s also Rome, Berlin, and Paris. In part, Europe’s national regulators seem motivated by a genuine desire to prevent abuse in their markets. In part, they are telling Brussels that they want to keep on playing a key role as Europe rolls out its new Digital Markets Act (DMA).

The DMA defines certain online service providers as “gatekeepers,” controlling access to specific markets. It lists a series of do’s and don’ts for them.  Under the current scope being debated in Brussels, most, if not all “gatekeepers” would be American companies that run online marketplaces, app stores, online search engines, social networking, and cloud services. Their mergers and acquisitions deals will receive additional scrutiny. According to the draft DMA  text, these large platforms enjoy an “entrenched and durable position, often as a result of the creation of conglomerate ecosystems around their core platforms services, which reinforces existing entry barriers.”

Although European leaders have agreed on a broad framework for the DMA, it’s now up to them, the European Parliament, and the European Commission to hammer out the details. In particular, it remains to be seen how enforcement will be divvied up between the European Commission and national regulators.

Companies fear becoming subject to 27 different interpretations of the new rules. Pro-Brussels advocates insist that they can provide a single coherent and consistent enforcement and can avoid the issues that emerged in recent years over the bloc’s landmark GDPR privacy law. GDPR gave Ireland and Luxembourg, home to the European headquarters of Google, Facebook, Microsoft, Apple, and Amazon, responsibility for enforcement – and few investigations took place.

National enforcers from Europe’s big countries respond that Brussels itself often has been too slow – it launched an antitrust investigation of Google in 2009 which is still being litigated in European courts.  And national officials believe they have the expertise required to impose effective punishment.

Germany’s cartel office announced earlier this month that it was investigating potentially anti-competitive practices related to Google’s processing of personal data. The cartel office, or Bundeskartellamt, is holding consultations with the search engine giant to discuss competition concerns related to Google News.

French data privacy regulators have issued fines of €150 million ($169 million) and €60 million ($67.6 million) against Google and Meta Platforms’ Facebook, respectively, over their policies on cookies. While the sites offer buttons to immediately accept cookies, they don’t offer an equivalent solution for easily refusing cookies, the CNIL, the Commission Nationale de lInformatique et des Libertés found.

Google said in a statement that it was “committing to further changes and active work with the CNIL in light of this decision.” Facebook said it was reviewing the decision and emphasized that users can revisit and manage their data controls at any time.

In Italy, the Amazon fine represents a watershed. There’s the amount – €1.13 billion with a “b.”  And there’s the precedent, targeting for the first time Amazon’s business model of bundling its vast logistics network and online marketplace to gain an advantage over competitors.

The Autorità Garante della Concorrenza e del Mercato, or AGCM, accused Amazon of providing unauthorized perks to sellers who used the platform’s Amazon Logistics. These sellers received unfair advantages such as improved visibility, higher search rankings, and better access to consumers through the Amazon Prime program and coveted “Buy Box.”

In addition to paying the fine, Amazon must define and publish a set of standards that make a seller eligible for Amazon Prime. The company must then “extend every privilege in terms of sales and visibility on the platform to all third-party vendors who respect the standards,” AGCM said.

About a year after Italy announced its investigation into Amazon’s logistics practices, the European Commission informed Amazon that it too had reached a preliminary finding that the “Buy Box” and Prime label breached EU antitrust rules by distorting competition in e-commerce.  But it has not yet announced a final judgment or punishment.

Amazon sued to try to stop the parallel investigations, but the European Court of Justice ruled in October that both could continue.

Amazon reportedly plans to appeal the Italian fine. “The proposed fine and remedies are unjustified and disproportionate,” a company spokesperson said in a statement.

Europe’s intention to impose strict regulation on US Big Tech long has been clear. But what remains unsure is whether it will impose a single, continent-wide enforcement mechanism or whether companies will have to manage the risk country-by-country. It’s a giant question. The answer will do much to determine whether the continent ever creates a unified digital single market.

Janna Brancolini is an American journalist and attorney based in Milan, where covers environmental and financial policy in Europe for Bloomberg and all things Italian for the Los Angeles Times.