Our Solar System is nothing special compared other stellar systems across the universe. Although we only have one star compared to other star systems such as Sirius which is a double star system, we do have planets which Sirius lacks.
In addition to planets, we have comets, objects that are made of ice and dust that when they approach the Sun, in our case, they burn off to produce a tail. The most well known one is Halley's whose orbit takes 76 years to go round the Sun. If you're a bit impatient then you could settle for Encke whose orbit is a mere 3.3 years. The comets that orbit our solar system are just known as comets and those that orbit other stars are referred to as Extrasolar Comets or Exocomets for short.
The first Exocomet to be discovered was in 1987, orbiting the star Beta Pictoris. The first exocomets were discovered by Spectroscopy, studying the light and radiation from the star. The star itself is a quite an insignificant star compared to other stars out there such as Rigel, also a Beta star. Beta stars are generally the second brightest star in the constellation, although Pollux is the brightest in the constellation of Gemini, the twins but has Beta designation. Wiki
Beta Pictoris is by no means the only star that has been found to have comets. Other stars that have comets in orbit are :-
It was announced by N.A.S.A. at the beginning of 2017, that they had detected a star in the constellation of Pavo, the Peacock where the comets were plunging into the star. The star is a mere 93 Light years from the Earth and is a very young star, 23 million years old compared to the Earth which is billions of years. To put it in context, the dinosaurs were extinct before the star was born.
It is believed that the cause of the comets plunging into the star is because of a yet unseen planet that deflected their course. The star is from the same stellar nursery that gave life to Beta Pictoris. The Beta Pictoris Moving Group as these stars are called are the closest group of young stars to the Earth. 37.5 percent of the massive stars in the group have a star in orbit round it such as 51 Eridani. Ref: N.A.S.A.
The easy to remember KIC 3542116 is a star that was studied by the kepler space telescope hence its designation. It made the news at the end of October 2017 when it was discovered that the star had six comets in orbit round the star. These stars are roughly the same size as Halley's Comet. The discovery was made not by a professional astronomer but a Citizen Astronomer.
A citizen astronomer is someone who is an amateur who professional organisation which in this case was Yale University to help sift through data that a computer might miss. If you've been put off from going to university to study astronomy and becoming a professional, this should be a useful reminder that you can make a discovery without having educational knowledge behind you.
The comets had been discovered by the dips in the brightness of the star. Comets are no bigger than a football pitch compared to planets and therefore are harder to spot. This same method is used to detect extrasolar planet (exoplanet) by studying the dips in the brightness. Ref: R.A.S.