"On my own" has been a phrase for a long time, for example:

I have suffered one on my own — A Spy on the Conjurer, 1725

Often there is erasure of the object, to prevent repetition:

Another's age, shall hasten on my own — The life of Alexander Pope, 1769

So no doubt the stand alone phrase is a growth from the erased type.

The OED has the phrase going back as far as 1404:

The Comunes desiren that the Kyng shulde leve upon his owne.

Where upon and on are synonymous in this context.

The two meanings the OED gives for the are:

a. In to live on (also upon) one's own: to live on one's own resources. Obs.
b. On one's own initiative, account, etc.; (now usually) alone, unaccompanied; by oneself.

b's meaning has examples going back to 1895.

Given meaning b, on's meaning seems to have evolved from the meaning as in "on my honour", which is about hands being on a bible.

From the OED's entry for on:

With or as with the hands touching (a bible, etc.), in making an oath; using or invoking as the basis of an oath, affirmation, etc.

"On my own" has been a phrase for a long time, for example:

I have suffered one on my own — A Spy on the Conjurer, 1725

Often there is erasure of the object, to prevent repetition:

Another's age, shall hasten on my own — The life of Alexander Pope, 1769

So no doubt the stand alone phrase is a growth from the erased type.

The OED has the phrase going back as far as 1404:

The Comunes desiren that the Kyng shulde leve upon his owne.

Where upon and on are synonymous in this context.

The two meanings the OED gives for the phrase are:

a. In to live on (also upon) one's own: to live on one's own resources. Obs.
b. On one's own initiative, account, etc.; (now usually) alone, unaccompanied; by oneself.

b's meaning has examples going back to 1895.

Given meaning b, on's meaning seems to have evolved from the meaning as in "on my honour", which is about hands being on a bible.

From the OED's entry for on:

With or as with the hands touching (a bible, etc.), in making an oath; using or invoking as the basis of an oath, affirmation, etc.

"On my own" has been a phrase for a long time, for example:

I have suffered one on my own — A Spy on the Conjurer, 1725

Often there is erasure of the object, to prevent repetition:

Another's age, shall hasten on my own — The life of Alexander Pope, 1769

So no doubt the stand alone phrase is a growth from the erased type.

The OED has the phrase going back as far as 1404:

The Comunes desiren that the Kyng shulde leve upon his owne.

Where upon and on are synonymous in this context.

The two meanings the OED gives for the are:

a. In to live on (also upon) one's own: to live on one's own resources. Obs.
b. On one's own initiative, account, etc.; (now usually) alone, unaccompanied; by oneself.

b's meaning has examples going back to 1895.

Given meaning b, on's meaning seems to have evolved from the meaning as in "on my honour", which is about hands being on a bible.

"On my own" has been a phrase for a long time, for example:

I have suffered one on my own — A Spy on the Conjurer, 1725

Often there is erasure of the object, to prevent repetition:

Another's age, shall hasten on my own — The life of Alexander Pope, 1769

So no doubt the stand alone phrase is a growth from the erased type.

The OED has the phrase going back as far as 1404:

The Comunes desiren that the Kyng shulde leve upon his owne.

Where upon and on are synonymous in this context.

The two meanings the OED gives for the are:

a. In to live on (also upon) one's own: to live on one's own resources. Obs.
b. On one's own initiative, account, etc.; (now usually) alone, unaccompanied; by oneself.

b's meaning has examples going back to 1895.

Given meaning b, on's meaning seems to have evolved from the meaning as in "on my honour", which is about hands being on a bible.

From the OED's entry for on:

With or as with the hands touching (a bible, etc.), in making an oath; using or invoking as the basis of an oath, affirmation, etc.