The distant future tense involves talking about distant future. Look at the examples given below to learn further.

यदि पृच्छति तदा गन्तास्मि
yadi pṛcchati tadā gantāsmi
If he asks, then I will go.

यदि पृच्छति तदा गन्ता
yadi pṛcchati tadā gantā
If he asks, then he will go.

The difference between the ordinary future tense and the distant future tense is that distant future tense does not depend on the present while the ordinary future tense depends on the present.
Now let us look at how these words are formed.

Formation:

The distant nouns are formed from tr noun and verb as look at the table given below to learn further. Even though it is based on a noun, this is a real verb form. Look at the table given below to learn further.
bhū (a+, P, distant future tense)

भू Singular Dual Plural
3rd Person भविता
bhavitā		 भवितारौ
bhavitārau		 भवितारः
bhavitāraḥ
2nd Person भवितासि
bhavitāsi		 भवितास्थः
bhavitāsthaḥ		 भवितास्थ
bhavitāstha
1st Person भवितास्मि
bhavitāsmi		 भवितास्वः
bhavitāsvaḥ		 भवितास्मः
bhavitāsmaḥ

Look at the observations given below:
In the first and second person: case singular and masculine –tr is used, this is followed by as which is inflected to show the person and the number of the verb.However, in case of the third person, we use first person endings instead of as, for the tr noun, no extra verb is used. This results in some ambiguity, look at the sentences given below to learn further.

स हन्ता
sa hantā
He is a killer.

स हन्ता
sa hantā
He will kill.

One has to depend on the context to understand whether something is a noun or a verb.
Distant future tense in Atmanaepada.

Distant future tense is truly rare, and usually, its forms are in parasmaipada. However, there are a few forms of Atmanepada which can be seen below.
Look at the table given below:
bhū (a+, A, distant future tense)

भू Singular Dual Plural
3rd Person भविता
bhavitā		 भवितारौ
bhavitārau		 भवितारः
bhavitāraḥ
2nd Person भवितासे
bhavitāse
 भवितासाथे
bhavitāsāthe
 भविताध्वे
bhavitādhve
1st Person भविताहे
bhavitāhe
 भवितास्वहे
bhavitāsvahe
 भवितास्महे
bhavitāsmahe