They only collect data of the installation process. Once installation is complete, no additional data is collected. They've even publicly released the results.
>The collected data is not-personally-identifiable. Meaning that a user cannot be singled out or tracked based on the data he/she provided. Here’s what Ubuntu collects
> Version and flavor of Ubuntu you’re installing
> Whether you have network connectivity at install time
> Hardware statistics such as CPU, RAM, GPU, etc
> Device manufacturer
> Country
> Installation time
> Whether you choose auto login, installing third-party codecs, downloading updates during install
> Disk layout