In Jain Dharma, Mahavir Swami has no living “rightful successor” in the current period.

A Tirthankar is not succeeded by another person as a spiritual ruler. Mahavir Swami was the 24th Tirthankar of this avasarpiṇī kaāl, and after his nirvāṇa, the Tirthankar lineage does not continue in the form of a worldly successor.

In the Jain tradition:

• The Ganadharas were his chief disciples during his lifetime.
• After Mahavir Swami’s nirvāṇa, the Shasan continued through sadhus, sadhvis, acharyas, upadhyayas, and shravaks/shravikas, but not through a single successor to Mahavir Swami.
• The next Tirthankar in this avasarpiṇī is traditionally believed to be Lord Parshvanath? No — Parshvanath was earlier, the next Tirthankar in the future is Lord Padmaprabhu? No — that is also not correct. In current Jain belief, the next Tirthankar will be Lord Padmnabha in the next uplifting period only after a very long time, not in the present era.

So, in simple terms:

There is no current successor to Mahavir Swami. His truth, teachings, and Shasan continue, but not through a single appointed successor.