Sentence Fragments

Hello, Steves,
Try googling, there are many hits.
Here's the first one:
[link]

Hello Steves5a

I would probably divide acceptable fragments into:

1. Those that are explicable in context.
2. Those that are used for effect.

For instance:

"Have you seen MissQ recently?"
"Fairly recently¹. Why do you ask?"
"No particular reason². What about MissP?"
"Likewise³."

Here, you can explain the first two fragments as ellipses, and the third as a 'ditto':

¹ "(I have seen her) fairly recently."
² "(There was) no particular reason (for asking)."
³ "I refer you to my previous response."

The second kind of 'acceptable' fragment is used in advertising¹ and a certain cheesy kind of journalism/literature²:

¹ English Forums. Good for grammar. Good for English. Good for you.

² Basingstoke, 2005. It was hot. D*mn hot. Too damn hot. Dust. Flies. Sweat. Accountants. People coming. People going. Prepared leaf salads in their shopping trolleys. And just one thing on everybody's mind. And then some. I moseyed over to the chick at the checkout. Hot. D*mn hot. Too damn hot. She held my gaze. Cool as a cucumber. But hot.

"Nectar card?"

I let my eyes slide over her full suave figure in its blue and orange checkout overall.

"Nope."

"Cashback?"

"Uh uh."

Sweat dripping down my back.

"Two pence. For your used bags."

{----------cut----------}

(You know the kind of thing.)

MrP