Provincial Courts were established by Lord Cornwallis as part of his administrative and judicial reforms in British India. These courts were set up to administer justice in the provinces and resolve civil and criminal cases. Lord Cornwallis established Provincial Courts at four places, namely Murshidabad, Calcutta, Patna, and Dacca.

1. Murshidabad:
The first Provincial Court was established in Murshidabad, which was the capital of Bengal at that time. Murshidabad was an important political and administrative center, and the establishment of a Provincial Court there aimed to provide easy access to justice for the people of the region.

2. Calcutta:
The second Provincial Court was established in Calcutta, the capital of British India. Calcutta was a major commercial and administrative hub, and the establishment of a Provincial Court there was crucial to ensure efficient administration of justice for the British administration as well as the local population.

3. Patna:
The third Provincial Court was set up in Patna, which was an important city in the province of Bihar. Patna had a significant population and was a center of trade and commerce. The establishment of a Provincial Court in Patna aimed to provide legal remedies and resolve disputes for the people residing in Bihar.

4. Dacca:
The fourth Provincial Court was established in Dacca, which was the capital of Bengal Presidency before it was shifted to Calcutta. Dacca was an important administrative and commercial center, and the establishment of a Provincial Court there aimed to provide access to justice for the people of the region.

In conclusion, Lord Cornwallis established Provincial Courts at four places - Murshidabad, Calcutta, Patna, and Dacca. These courts were set up to ensure the efficient administration of justice and resolve civil and criminal cases in the respective provinces.