Under MiFID post-trade transparency rules, equity trades must be published within a minute for market price-forming purposes. In practice, this is the trade reporting function whereby a trade is submitted to an exchange, or APA reporting service. They publish it as market data which participants in turn can consume.
On-exchange trades publish with an exchange identifier (MIC). Off exchange trades publish with the MIC of a systematic internaliser (SI), or with XOFF.
If a MiFID firm trades outside of Europe and the instrument is in scope, that is, listed on an EU exchange, then the trade needs to be published in Europe. However, not all on-venue trades in third countries must be reported in the EU. If the venue has been assessed as having a similar regime, the trade is recognized as already published. ESMA maintains a list of these recognized third country venues for post-trade transparency purposes. For any venue not on the list a XOFF trade needs to be published in Europe.
In early November 2020, ESMA included UK venues on the list of their positive assessments ahead of January. This was the answer the industry had been hoping for as it would avoid thousands of extra trade reports post-Brexit.
The MiFID share trading obligation (STO) is a different proposition, concerned with where EU trading can take place. Whether the European Commission will grant stock market equivalence to the UK is yet to be seen.