Almost all grapeships are owned by modosophont groups and individuals, rather than by transapients. Most modern examples use conversion drive technology which has percolated down from transapient level-tech. Interstellar grapeships which use wormholes require permission from the Nexus Archai to do so, but this permission may be withdrawn at any time.
Grapeship ownership varies according to polity, situation, and local laws and regulations. There are big transport and passenger corporations, as well as ships run by clades and their organisations. Private ships fill in the gaps and run the odd errands and tourist lines.