For a spell such as mass conviction, which targets "Allies in a 20-ft.-radius burst", is there a single one-time determination of who is targeted, based on which allies are within 20 feet of the caster at the time of casting, or is it a spell effect that moves with the caster, and any ally who happens to be within 20 feet of the caster when they need to make a saving throw would have the benefit for that round?
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The burst happens at the moment of casting, by RAW it means you can run away from the caster and keep the buff as long as it lasts. Take a look at the non-burst example, It does not state that you cannot get away or loose the effects if you do so..
It has to state "continuous emanation" and specifically say it ends when you go away.
Take Invisibility Sphere for example
It's one-time. Compare Magic Circle Against Evil - it doesn't target "people around the caster," it targets the caster and exists as a 10' emanation so people moving in and out of it get the benefits. But if it targets other people, then that just means it gets applied to them then lasts for the duration. Bless is a good example of the "no, it just went off in a burst, someone showing up later doesn't get it" spell.
The easiest way to tell is to look in the "Area" or "Target" descriptor of the spell.
If the spell states that the area is a 10ft Emanation (think magic circle), the area is centered on either a location, an object, or the target of the casting and anyone moving more than 10ft from that location, object, or target loses the effect of the spell up until the duration of the spell ends.
If the spell states that the target is a 10ft Burst (think fireball), Anyone within the area at the time of the casting receives the effect, the spell takes effect instantaneously, and persists on anyone who was within 10ft of the target at the time of casting until the duration of the spell ends.