What I mean is: did it have an ending point beyond either Valinor or the Land of the Sun when it was flat before the destruction of Númenor or was it just flat?
I don't mean to say it has boundaries afterwards; I'm just talking about before.
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Yes it did.
From the above map, taken from Karen Wynn Fonstad's Atlas of Middle-earth, we see that the lands were surrounded by Ekkaia, the Encircling Sea, a immense and dark ocean that seemingly went on forever, although it was bounded on its far side by the Walls of Night (a vast transparent barrier that separated Arda from the Timeless Void outside). It was distinct from Belegaer, the ocean that lay between Aman and Middle-earth, though it was said that the waters did meet in the far north.
It was from the far north that Melkor returned to the world, scaling the Walls in secret, and building his first fortress of Utumno in the cold and bleak places where the Walls were nearest to land.
There was a place, in the extreme West, where the Walls and Ekkaia could be passed between, a location called the Door of Night. It was through this door that Melkor was thrust when he was exiled. There was a similar structure in the furthest East known as the Gates of Morning, through which the Sun was said to rise each day. These gates were located in a mountain range known as the Walls of the Sun. The Gates themselves were actually seen by Númenórean sailors from their ships as they voyaged around Middle-earth, so they must have been enormous and very impressive. Whether either of these structures remained after the world was changed is unknown.