The Attribution Reporting API currently supports last-touch attribution. This model gives all the credit for a conversion to the last ad interaction (click or view) that occurred before the conversion.
Attribution Reporting also allows for some flexibility in setting conversion priorities, which can influence how credit is assigned in cases where multiple ad interactions occur. This GitHub article shares more information about the flexibility in priority setting.
Cross-platform attribution
Currently, the API supports same-device, cross-platform attribution. This means that it can track conversions that happen across different platforms (like web and app) as long as they occur on the same device.
More information on the types of cross-platform attribution flows can be found in the developer documentation. As stated in the public update, app-to-web attribution is available in Chrome and Android for origin trials.
Future developments
If other attribution models are critical for your use case, Chrome encourages the ecosystem to open an Issue to request support for those models. Additionally, there is a bi-weekly meeting open to W3C Web Incubator Community Group members (free to join) during which you can raise this as an agenda item to discuss.