There are two different "kinds" of Toon monsters that behave slightly differently. The newer Toon monsters state the following:
While you control "Toon World" and your opponent controls no Toon Monsters, this card can attack your opponent directly.
So as long as you control "Toon World", a Toon monster can attack your opponent directly even if they control monsters.
However, the older Toon monsters and "Manga Ryu-Ran" state:
This card can only be Special Summoned while you control "Toon World". ...When "Toon World" is destroyed, destroy this card. If your opponent doesn't control a Toon Monster, this card can attack your opponent directly. If your opponent controls a face-up Toon Monster, you must select it as an attack target.
Unlike the newer Toon monsters, these monsters can attack directly even if "Toon World" is not on the field. This is because if "Toon World" is removed from the field other than by being destroyed (returned to your hand, returned to your deck, etc.), your Toon monsters will not be destroyed as well. And since there is no requirement for "Toon World" to be activate so they can direct attack, they can do just that.
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Toon Monsters can attack directly if the opponent has no Toons, but if he does have one, the turn player's Toon must attack it (if he attacks at all, that is). No other part of the show's Toon rules are applied. The Toon controller's life points are not protected in any way. A player's non-Toon may freely attack the other player's Toons or non-Toons, and damage calculation will proceed as normal. If the Toon Monster is too strong, then you will need to destroy it with an effect first. A monster that can attack directly, can do so even if the other player has a Toon monster. Toon Monsters do not interact in any way with direct damage, so cannot stop burn damage from cards like Chain Burn.
It's probably a mix-up with the anime effect. In the card games, Toon Monsters have no protection against being attacked.
The yugioh card "toon world" does nothing unless you have toon monster cards.Toon world is required for you to activate them and put them into play.
I honestly think Pegasus's deck would be better due to the face that Toon monsters can attack directly if your opponent does not control a Toon monster. It's only downfall is that for most Toon cards, you need Toon World on the field. To prevent Toon World's destruction, I suggest cards like Dark Bribe or Solemn Judgement or even (if you can get it on the field) White Dragon Ninja. I find that Pegasus's deck is better also because Joey's deck is based around cards with luck, and luck shouldn't be relied on all of the time in Yu-Gi-Oh.
A Toon World Deck is soley dependent on the Continuous Spell Card Toon World. A "Cartoon Network" Deck, as it is dubbed, can be very competitive if the right cards are drawn at the right time. Because the cards so heavily rely on Toon Worldto gain their more beneficial effects, Players often utilize cards such as Magic Reflector and Dark Bribe. Toon Decks also are centered around their only "Class B" Toon, Toon Dark Magician Girl. It is usually either this card, or Toon World that is the "Trump Card" of the Deck.It is also highly recommended that Players always run three copies of Toon Table of Contents. This is considered to be the Deck's "Searcher Card". It is also not advised to run any copies of Manga Ryu-Ran, as it requires as many Tributes as Blue-Eyes Toon Dragon, but with considerably less ATK.Since Toon Monsters are almost always sent to attack the opponent directly, they are very vulnerable to cards such as Mirror Force or Sakuretsu Armor. Therefore, it is recommended that Players add Royal Decree and Giant Trunade in the Deck.It is also helpful to add cards that gain Life Points, Solemn Wishes most notably. Solemn Wishes usually deals with the massive amounts of Life Point payments used by the Toon Monsters.Because most Toon Monsters are Special Summoned, this allows for the use of cards such as Dandylion and Scapegoat, as the card lore for Dandylion only states that "...the Tokens may not be used for a Tribute Summon in the same turn..." This implies that there are no restrictions for Toon Monsters, as they are Special Summoned.For more information and strategies concerning the Toon Deck, click on the "Related Link" below.