I did a triptych of a panorama looking over a 40 mile wide plain. Each panel was 12 x 16 inches, and hanging them I left a gap of about half an inch between each panel. There were no frames around the panel.
The paintings were done so that if they were all place touching each other, there would be no discontinuities in the panorama.
The panels look better if there is a focal point in each of them - in other words, I think each panel should look complete if shown by itself.
David Hockney has done some huge multi panel paintings, including one of the grand canyon - see link.
Religious triptychs often have the centre panel bigger than the side panel, and there is usually a frame round each panel. Sometimes side panels would be hinged, and the complete triptych might only be visible when the panels were opened up on religious feasts. See this example by Rubens in the cathedral in Antwerp.