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The errant planet is similar in size with the star and it's made all of water. Usually is icy, but probably gonna melt when approach the star.

What happens during the process of collision between the star and the planet?

I didn't care about the size, just need to be similar. Points extra for different examples and examples with different sizes.

Question related: Could a planet made completely of water exist?

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    $\begingroup$ Planets as big as stars don't exist, and that's pretty certain. Jupiter is about as big as planets come, since heavier ones are squeezed smaller by their own gravity. Yes, this would apply to one made entirely of H2O; it's not that incompressible. $\endgroup$ – John Dallman Sep 29 '16 at 15:17
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    $\begingroup$ @JohnDallman It is possible en.wikipedia.org/wiki/White_dwarf and en.wikipedia.org/wiki/Neutron_star and the star could actually be much smaller than the planet. $\endgroup$ – Vincent Sep 29 '16 at 22:36
  • $\begingroup$ Can someone explain why all the negative votes? I didn't want to repeat the errors. Thanks. $\endgroup$ – Malkev Sep 30 '16 at 7:07
  • $\begingroup$ You could ask the question here because few people are going to notice your comment: meta.worldbuilding.stackexchange.com $\endgroup$ – Vincent Oct 2 '16 at 15:32
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This is actually a bit tricky, because size does matter to some degree.

The big problem is when planets get to stellar-mass sizes, they more than likely are beginning deuterium fusion, which can turn them into at least brown dwarfs, which are failed stars.
Smaller than that, a water world of that size would likely be a gas giant with a watery atmosphere. If that's the case, then the atmosphere would evaporate away, leaving a misty trail of water as it orbits. (See the Exoplanet HD 209458b for an IRL example.)

As for the actual effects, here's my best guess at a blow-by-blow coverage. I'm assuming an all-water planet, no orbit (just the planet making a beeline for the star), and ignoring any/all planetoids it may encounter along the way.

The Approach
Assuming the planet originated far away, as it nears the star, the icy exterior begins to melt. If the planet is large enough, water on the surface will begin to form oceans, and tune an atmosphere. Water closer to the core will be so heavily compressed, it'll be crushed into exotic ice forms, like Ice-7 and the like.

As it gets closer and closer, more and more water will begin to evaporate. Eventually, the planet will be covered in a thick atmosphere, like a watery version of Venus. Eventually, more heat and pressure (as well as the lack of a decent magnetic field) causes the atmosphere to become so bloated, it begins to float away. Like a comet drawing close to the Sun, the atmosphere boils and evaporates away, leaving a ghostly trail behind it. Depending on the speed, by the time the planet reaches the Roche limit, it may lose all of its oceans amd atmosphere this way.

Final Approach/Impact
Passing into the Roche limit, the superheated icy sphere begins to crack and splinter due to tidal forces. Whole chunks of Ice-7 and Ice-3 fly away from both the near and far sides of the planet as it draws nearer and nearer. When it impacts, it does so as a swarm of hardened ice crystals, rather than as a whole object, peppering the star's surface.
The impact as a whole does little to affect the star. At most, the relatively minuscule addition of mass causes the star to burn slightly brighter. About 1,000~ish years are taken off the star's lifespan, and everyone watching from afar wonders why the star seemed to pulse briefly.

So that's my rough, half-educated guess as to what'd happen. Feel free to correct me if I made any mistakes, as I'm not too familiar with the properties of exotic ices. '^^

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Nothing different than a dry planet hitting the star - it'll certainly be dry before it hits.

It'll look like a large comet - moving with a stream of steam being left in it's wake.

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