Gillian, having looked at your material it strikes me that the reason is quite simple.
Martha Seaman/Voce is a distraction, a red herring*.
Emma Larkin was a blood relative of the three people to whose estates she was granted administration in 1904. Martha wasn't a blood relative to any of them.
If an estate or estates are left unadministered because the nominated original administrator dies, or refuses the burden, or for any other reason, the nearest living blood relative of the testator has the prima facie case to apply for and be granted the administration.
It may be that in 1904 Emma Larkin was the nearest living blood relative of these testators.
However, this raises the question of why the estates remained unadministered until 1904.
It may be that this had something to do with Martha (hence my asterisk above).
There's no point in speculating on this in a vacuum. If you want to get to the bottom of this, the place to start is with the documentation of the grants to Emma Larkin in 1904.
With luck, it will mention in whose place Emma Larkin has become the administrator.
One of my relatives died intestate and childless in Edmonton in 1891. His administration was granted to his nephew; described as "the lawful nephew and one of the persons entitled in distribution to the personal estate".
The grant document notes that the intestate's "natural and lawful sister and only next of kin of the said intestate" had renounced the administration.