Gerund Diagramming Help

Tyler's singing filled the hall with melodious tunes ringing in our ears?
I understand everything after beyond the gerund phrase. How is "Tyler's singing" diagrammed? Is Tyler's an adjective going under the gerund singing or is Tyler's the possessive pronoun subject of the gerund singing?
Same example in this sentence:
Sarah and Sean's handling of the situation gave their parents cause for great joy and celebration.
Again:
Steffan's giving a gift to Stephanie greatly surprised the smiling young woman.
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Are they diagrammed as subjects of the gerund or adjectival modifiers?
Assistance greatly appreciated. Thanks

[Lynque]

Tyler07,
A gerund is a verb-made-noun-by-adding-ing (drive, driving)and, as such, can appear in sentence as subject or object. As a noun, it has more to do with thing or idea than with person or place.

In diagram, it appears on a horizontal 'stairstep' line instead of a straight one:
like this:
_________
|__________

[Lynque]

Tylero7,
A gerund is a verb-made-noun-by-adding-ing (drive, driving)and, as such, can appear in sentence as subject or object. As a noun, it has more to do with thing or idea than with person or place.

In diagram, it appears on a horizontal 'stairstep' line instead of a straight one:
like this: _________
|__________

[Lynque]

Sorry, Tyler, neither of these worked. Just think a a horizontal line with one stairstep down. Write your gerund over the step.