Gollum's boat??

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Originally Posted by alatar

I'm becoming more unhinged...

Glad to be of service.

It's surprising that he uses a log when pursuing the Fellowship down the Anduin, as I assume then that he couldn't steal a boat nor build something while he waited for the Fellowship to leave Lothlorien.

Oh but if he built one of his trademark boats he'd be caught, surely. A floating log among others doesn't catch anyone's attention, making it the perfect vessel for this purpose.