if cyber phoenix is equpped with premature burial and my opponent plays heavy storm, will the phoenix be destroyed by prematures effect?

Yes..................................................................

But how? What about the part of premature burial that says " when this card is destroyed, destroy the equipped monster"? - is that a continuous effect, or one that triggers when premie is destroyed?

This belongs in the card ruling section, NOT the Strategy, Tactics & Card Discussion. As for why, you'll have to ask HalfDemonInuyas. He'll know...

This happen:
You play Premature Burial, SS Cyber Phoenix.Then Cyber Phoenix negates and destroys Premature Burial.no case for Heavy Storm

However, If you play Call of the Haunted to call Cyber Phoenix back as chain to Heavy Storm, Cyber Phoenix stays on the field

What X-Elemental posted was correct, but in answer to your last question, the destruction effect of Premature is a triggered effect. It happens when Premie is destroyed.

Oooooh, so THAT is the answer to life. Oh, wait, wrong forum! Tee hee. Thanks, X and Squid. ^_^

Ok from what i read, heres what happens

I activate premie and target cyber phoenix in the grave

Cyber phoenix comes out (it doesnt negate premies targeting while its in the grave)

Cyber phoenix is sp summoned and destroyes premie

Now does the phoenix stay?

If not, then why?

Cyber Phoenix does stay on the field. Consider its effect to be synonymous with Freed the Matchless General, then look at Freed's 3rd ruling. It should help you to compare and identify the proper procedure. :)

Just a little clarification for you...

Cyber Phoenix does NOT "destroy" anything. All it does is negate the effects (like Imperial Order for Magic and Royal Decree for Trap and such)

yes, so premature burial would remain equipped to cyber phoenix, since nothing is destroying it and nothing is preventing it from remaining equipped to the phoenix (its just being negated) and since premature burial doesn't actually do anything while its equipped it doesn't matter.

then when premature burial is destroyed, if cyber phoenix is still in attack position it will not be destroyed. but if cyber phoenix is in defense position when pb is destroyed then cyber phoenix will no longer negate premature burial and will be destroyed with it.

its slightly different than freed, since freed always destroys pb while its still negating it, while the cyber phoenix may not be negating pb when it gets destroyed.

its also different than things like call/spellbinding circle that "loose their attachment" when negated and never regain it, equips will still be and remain equipped even if negated and will reapply their effects if they are no longer negated.