Answer by taking a quote from the following article:

King Diamond are a Danish heavy metal band formed in 1985 by vocalist King Diamond, guitarists Andy LaRocque and Michael Denner, bassist Timi Hansen and drummer Mikkey Dee. Diamond, Denner and Hansen had recently departed the group Mercyful Fate, and decided to form a new band under the King Diamond moniker, as it was already known from the Mercyful Fate days. In 1986, King Diamond released their debut album Fatal Portrait. Since then the band have released a total of twelve studio albums (most of them concept albums), two live albums, two extended plays, five compilations and five singles.

The band was formed in 1985 by vocalist King Diamond, guitarist Michael Denner and bassist Timi Hansen. The three had recently departed from the group Mercyful Fate, which fell apart due to musical differences between King Diamond and guitarist Hank Shermann. According to Diamond, when he, Denner and Hansen decided to form a new band, they chose the name "King Diamond" to "get better deals", and because the name was already known from Mercyful Fate. To round-out the line-up of the King Diamond band, the group chose drummer Mikkey Dee and guitarist Andy LaRocque. In July, 1985, the band began recording their debut album at Sound Track Studio in Copenhagen, Denmark. On December 25, they released their debut single "No Presents for Christmas". Fatal Portrait, the band's first full-length studio album, was released on February 17, 1986, through Roadrunner Records. Produced by Rune Hoyer and vocalist King Diamond, the album charted at number 33 on the Swedish album chart, and spawned the single "Halloween", which was released on June 6, 1986. In December 1986, King Diamond began recording their second studio album, once again at Sound Track Studio in Copenhagen, Denmark. Prior to the album's release, the group released the single "The Family Ghost" on July 1, 1987, for which they also shot their first music video. On October 21, 1987, King Diamond released the album Abigail, their first concept album based on an original story by vocalist King Diamond. The album went on to chart at number 39 in Sweden, number 68 in the Netherlands, and at number 123 on the Billboard 200. Following Abigail's release, guitarist Michael Denner left the band due to touring strains. He was subsequently replaced by Mike Moon for the album's supporting tour, during which the band recorded the live album In Concert 1987: Abigail (however it wasn't released until 1990).

What singles did they release?
On December 25, they released their debut single "No Presents for Christmas".