Good Question!
By default - all words are stored in the users browser cache - and no-one else is affected.
Look at the AddWordsToDictionary property of your SpellButton or SpellTextArea.
To allow 'Server' dictionary entries to be written - add: to web.config
<appSettings> .... <add key="aspnetspell_usecentraldictionary" value="True" />
// javascript code livespell.userDict.add(strWord);
The words are stored in accordance with the AddWordsToDictionary property of the last ASPNetSPell control on your web page/form.
You can download the Dictionary Encoder Application to create your own .dic dictionary files.