Here are types of pre-emption rights as per law:

Types of Pre-emption Rights
1. Pro-rata Pre-emption Rights: Existing shareholders have the right to purchase a proportionate amount of new shares.
2. Full Pre-emption Rights: Existing shareholders have the right to purchase all new shares.
3. Partial Pre-emption Rights: Existing shareholders have the right to purchase a portion of new shares.
4. Optional Pre-emption Rights: Existing shareholders may choose to purchase new shares, but are not required to do so.
5. Mandatory Pre-emption Rights: Existing shareholders are required to purchase new shares.
6. Priority Pre-emption Rights: Existing shareholders have priority to purchase new shares over new investors.
7. Tag-Along Pre-emption Rights: Existing shareholders can require the company to purchase their shares if another shareholder sells their shares.

Securities Laws and Regulations
1. Securities Act 1933 (US): Requires pre-emption rights for existing shareholders in certain securities offerings.
2. Securities Exchange Act 1934 (US): Regulates pre-emption rights for publicly traded companies.
3. European Union’s Prospectus Directive: Requires pre-emption rights for existing shareholders in EU member states.
4. Canada’s Securities Act: Regulates pre-emption rights for publicly traded companies.

Company Law
1. UK Companies Act 2006: Requires pre-emption rights for existing shareholders in certain circumstances.
2. Australia’s Corporations Act 2001: Regulates pre-emption rights for publicly traded companies.
3. Singapore’s Companies Act: Requires pre-emption rights for existing shareholders in certain circumstances.

Stock Exchange Rules
1. New York Stock Exchange (NYSE): Requires pre-emption rights for publicly traded companies.
2. London Stock Exchange (LSE): Regulates pre-emption rights for listed companies.
3. Toronto Stock Exchange (TSX): Requires pre-emption rights for publicly traded companies.

International Standards
1. International Financial Reporting Standards (IFRS): Requires disclosure of pre-emption rights.
2. Organisation for Economic Co-operation and Development (OECD): Recommends pre-emption rights for publicly traded companies.

Key Considerations
1. Regulatory compliance
2. Tax implications
3. Shareholder agreement
4. Board approval
5. Transparency
6. Disclosure requirements
7. Shareholder approval
Consult with legal, financial, and regulatory experts to ensure compliance and optimal design of pre-emption rights in your jurisdiction.