[Sheena]

I have a few medium size poppies and some little tiddlers, I'm just wondering if I need to remove the dead flower heads and stalks?

They are still flowering but the dead stalks are outnumbering the flowering ones...

[agapanthus]

I would....it may extend the life of the poppy

[Trillium]

But if you want more poppies, leave the 'dead' stalks as is; they're preparing seed for dispersal from those little shaker holes. Once the last of the flowers 'dies' then the whole plant goes dormant for the season. They're not rebloomers.