Answering step‑by‑step in very simple language.

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1. Can an abhavya jīv have a desire to become a Tirthankar?

• Abhavya jīv = soul which will never attain moksha. It will never get samyag darshan (right faith).
• Because it never gets true right faith, it also never walks fully on the path that leads to moksha or to Tirthankar‑hood.

So:

• An abhavya jīv may think in the mind:

“It would be nice to be a Tirthankar, or a great guru, or a god, etc.”

• But this is only an ordinary wish, mixed with ignorance or worldly motives (fame, respect, power, etc.).
• It is not the pure, spiritual icchā (desire) which becomes a real cause for Tirthankar‑nāma‑karma.

In other words:

• Yes, an abhavya can “want” it in a casual or proud sense.
• But that wish has no power to lead to real Tirthankar‑hood, because the soul itself is not capable of moksha.
• Only a Kevali (omniscient) really knows who is bhavya / abhavya; we should never label anyone in practice.

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2. Can a mithyādṛṣṭi but bhavya jīv have such a desire?

Break the terms:

• Bhavya jīv = capable of moksha (has the capacity to one day get right faith, right knowledge, right conduct).
• Mithyādṛṣṭi = currently in a state of wrong belief (no right faith yet).

So a “mithyādṛṣṭi bhavya jīv” means:

• The soul can attain moksha in some future birth,
• But right now it is in wrong belief.

About desire for Tirthankar‑hood:

1. As a present mithyādṛṣṭi (wrong believer):

- It can also think or wish: “I want to become a Tirthankar.” - But since it does not yet have samyag darshan, this wish is usually: - Mixed with pride, ego, or worldly thinking, or - Based on wrong understanding (seeing Tirthankar as a “high position”). - In this condition, the wish does not bind Tirthankar‑nāma‑karma.

1. When the same bhavya jīv later attains samyag darshan and high purity:

- Then, if a very pure, selfless icchā for Tirthankar‑hood arises, - Together with other very strong śubh bhāvs (pure feelings), - And with special types of supreme dān, śīl, tapa, bhakti, etc., - Then it can become the cause for Tirthankar‑nāma‑karma in that or some future human birth.

So:

• A mithyādṛṣṭi bhavya jīv can have the thought, but it becomes spiritually effective only when the same soul reaches right faith and great purity.

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3. Who can truly have the desire to become a Tirthankar?

From Jain viewpoint, in a real, spiritually valid sense, this desire belongs only to:

1. Bhavya jīvs (souls capable of moksha),
2. In human birth,
3. Who have at least some level of right faith (samyag darshan),
4. And whose desire is:

- Very pure, without ego or worldly craving, - Filled with compassion for all souls, - Along with very high puṇya and special qualities.

Scriptures describe:

• Tirthankar‑hood depends on the special Tirthankar‑nāma‑karma.
• This karma is extremely rare, and is bound only when:

- The soul is bhavya, - Has right faith, - Performs very extraordinary punya‑karmas with very pure inner feelings.

So, in full sense:

> Only a bhavya jīv with right faith and very high purity can “truly” have that desire which becomes the seed for becoming a Tirthankar.

Others may “wish” it, but it stays just a thought, not a cause.

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4. What does “having a desire to become a Tirthankar” really mean?

Many people misunderstand this. They think:

> “Tirthankar becomes like a king of religion; so I want that status.”

This is wrong understanding.

In Jain dharma, the true desire for Tirthankar‑hood means something like:

1. Intense desire for total purity:

- “I want to completely destroy anger, pride, deceit, greed.” - “I want to become totally vītarāg (free from attachment and aversion).”

1. Supreme compassion (karuṇā):

- “I want to help infinite souls by showing them the true path.” - Not by changing their karma, but by teaching and being an ideal example.

1. No ego, no demand:

- It is not: “I should be special, I should get respect.” - It is: “If it is according to my karmas, may I attain such a state where I can be most useful for others’ liberation.”

1. Strong, steady shubh bhāva:

- Continuously doing: - Pure dān (charity) without pride, - Śīl (moral conduct, vows), - Tapa (austerities), - Bhakti (deep reverence to Arihant, Siddha, Acharya, etc.), - With the inner feeling: > “May my soul become capable of such supreme state as a Tirthankar, for the good of infinite jīvs.”

1. Result:

- When such bhāvs are extremely strong and pure, Tirthankar‑nāma‑karma is bound. - In its fruition (in a future human birth, in the proper time‑cycle and kṣetra), the soul becomes a Tirthankar.

So, having that desire in Jain sense means:

> A very pure, selfless, compassion‑filled inner wish to attain the Arihant state that guides countless souls, > supported by matching conduct, austerity and virtues.

Not just a casual thought, not an ambitious dream.

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5. Summary in very simple lines

• Abhavya jīv

- Can imagine or wish: “I want to be Tirthankar,” - But this wish never leads to actual Tirthankar‑hood, because that soul can never attain moksha.

• Mithyādṛṣṭi bhavya jīv

- Can also think like this today. - But only when it later gets right faith and great purity, the same soul can have a true, effective desire and bind Tirthankar‑nāma‑karma.

• Who really has such a desire?

- Only bhavya souls, in human birth, with right faith and very pure, compassionate bhāva, - Free from ego and worldly motives.

• Meaning of that desire:

- Not wanting a “high post,” - But wanting perfect vītarāgata and maximum ability to show the path of moksha to infinite souls.

For more on bhavya and abhavya jīvs in simple language, you can read here