Great question! It seems like a bit of both:

In these progresses, the king was accompanied not only by his courtiers but by maesters and septons as well. Six maesters were often in his company to advise him upon the local laws and traditions of the former realms, so that he might rule in judgment at the courts he held. Rather than attempting to unify the realm under one set of laws, he respected the differing customs of each region and sought to judge as their past kings might have. (WOIAF)

However, these traditions were then blended in with new decrees from the Iron Throne into a common law; for example, see “The “rule of six,” now part of the common law, was established by Rhaenys as she sat the Iron Throne while the king was upon one of his progresses.”

In the reign of King Jaehaerys I, this changed:

“With Barth’s aid and advice, King Jaehaerys did more to reform the realm than any other king who lived before or after. Where his grandsire, King Aegon, had left the laws of the Seven Kingdoms to the vagaries of local tradition and custom, Jaehaerys created the first unified code, so that from the North to the Dornish Marches, the realm shared a single rule of law.” (WOIAF)

As I’ve said before, it’s entirely unclear how this legal code is enforced, or how this code brought the different legal traditions of seven kingdoms plus the accretions of two generations of Targaryens into harmony. However, it’s quite likely that the previous “common law” was the foundation of Jaehaerys’ Code, which was revised in the reign of King Viserys II.