While China is always painted as the bad guy for claiming most of the South China Sea it is usually forgotten Taiwan makes the same claim.
The writers at Wiki advise:
"The nine-dash line, at various times also referred to as the ten-dash line and the eleven-dash line (by [Taiwan]), is the demarcation line used by [China] for their claims of the major part of the South China Sea.[1][2]"
See map below:
The nine-dash line depicted here as a red line covers most of the South China Sea. Both China and Taiwan claim islands and waters within that line. Note some other East Asian countries have contested and/or semi-overlapping claims. (Map Voiceof America, 2012).
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"After evacuating to Taiwan, [Taiwan’s Government] has continued its claims, and the nine-dash line remains as the rationale for Taiwan's claims to the Spratly and Paracel Islands. Under President Lee Teng-hui, [Taiwan] stated that "legally, historically, geographically, or in reality", all of the South China Sea and Spratly islands were [Taiwan’s] territory and under [Taiwanese] sovereignty, and denounced actions undertaken there by Malaysia and the Philippines, in a statement on 13 July 1999 released by the foreign ministry of Taiwan.[31] Taiwan and China's claims mirror each other.[32] During international talks involving the Spratly islands, [China] and [Taiwan] have cooperated with each other since both have the same claims.[32][33]"
Pete Comment
A major difference is China has the military power to enforce many of its South China Sea claims, while Taiwan doesn’t.
Also the US may advise Taiwan’s government not to voice seemingly extravagant South China Sea (nine-dash line) claims.